Maxima – 169 – Teoria dei numeri – 1

ftc0

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.513.

Funzioni e variabili

bern (n)
Returns the n’th Bernoulli number for integer n. Bernoulli numbers equal to zero are
suppressed if zerobern is false.

(%i1) zerobern: true$

(%i2) map (bern, [0, 1, 2, 3, 4, 5, 6, 7, 8]);
                           1  1       1      1        1
(%o2)                [1, - -, -, 0, - --, 0, --, 0, - --]
                           2  6       30     42       30
(%i3) zerobern: false$

(%i4) map (bern, [0, 1, 2, 3, 4, 5, 6, 7, 8]);
                        1  1    1   1     1   5     691   7
(%o4)             [1, - -, -, - --, --, - --, --, - ----, -]
                        2  6    30  42    30  66    2730  6

bernpoly (x, n)
Returns the n’th Bernoulli polynomial in the variable x.

bfzeta (s, n)
Returns the Riemann zeta function for the argument s. The return value is a big float (bfloat); n is the number of digits in the return value.

bfhzeta (s, h, n)
Returns the Hurwitz zeta function for the arguments s and h. The return value is a big float (bfloat); n is the number of digits in the return value.

The Hurwitz zeta function is defined as

169-0

load ("bffac") loads this function.

burn (n)
Returns a rational number, which is an approximation of the n’th Bernoulli number for integer n. burn exploits the observation that (rational) Bernoulli numbers can be approximated by (transcendental) zetas with tolerable efficiency:

                   n - 1  1 - 2 n
              (- 1)      2        zeta(2 n) (2 n)!
     B(2 n) = ------------------------------------
                                2 n
                             %pi

burn may be more efficient than bern for large, isolated n as bern computes all the Bernoulli numbers up to index n before returning. burn invokes the approximation for even integers n > 255. For odd integers and n <= 255 the function bern is called.

load ("bffac") loads this function. See also bern.

chinese ([r_1, ..., r_n], [m_1, ..., m_n])
Chinese remainder theorem.

Solves the system of congruences x = r_1 mod m_1, ..., x = r_n mod m_n. The remainders r_n may be arbitrary integers while the moduli m_n have to be positive and pairwise coprime integers.

(%i5) mods : [1000, 1001, 1003, 1007];
(%o5)                      [1000, 1001, 1003, 1007]
(%i6) lreduce('gcd, mods);
(%o6)                                  1
(%i7) x : random(apply("*", mods));
(%o7)                            685124877004
(%i8) rems : map(lambda([z], mod(x, z)), mods);
(%o8)                          [4, 568, 54, 624]
(%i9) chinese(rems, mods);
(%o9)                            685124877004
(%i10) chinese([1, 2], [3, n]);
(%o10)                      chinese([1, 2], [3, n])
(%i11) %, n = 4;
(%o11)                                10

cf (expr)
Computes a continued fraction approximation. expr is an expression comprising continued fractions, square roots of integers, and literal real numbers (integers, rational numbers, ordinary floats, and bigfloats). cf computes exact expansions for rational numbers, but expansions are truncated at ratepsilon for ordinary floats and 10^(-fpprec) for bigfloats.

Operands in the expression may be combined with arithmetic operators. Maxima does not know about operations on continued fractions outside of cf.

cf evaluates its arguments after binding listarith to false. cf returns a continued fraction, represented as a list.

A continued fraction a + 1/(b + 1/(c + ...)) is represented by the list [a, b, c, ...]. The list elements a, b, c, ... must evaluate to integers. expr may also contain sqrt (n) where n is an integer. In this case cf will give as many terms of the continued fraction as the value of the variable cflength times the period.

A continued fraction can be evaluated to a number by evaluating the arithmetic representation returned by cfdisrep. See also cfexpand for another way to evaluate a continued fraction.

See also cfdisrep, cfexpand, and cflength.

Nota: non riesco a riprodurre gli esempi della Reference, ottengo errori sulle radici p.es: “cf: argument of sqrt must be an integer; found [0, 11] — an error. To debug this try: debugmode(true);“. Modifico gli esempi, semplicandoli.

expr is an expression comprising continued fractions.

(%i1) cf ([5, 3, 1]*[11, 9, 7]);
(%o1)                          [58, 3, 11, 1, 6]
(%i2) cf ((3/17)*[1, -2, 5] + (8/13));
(%o2)                      [0, 1, 2, 3, 1, 3, 6, 2]

cflength controls how many periods of the continued fraction are computed for algebraic, irrational numbers.

(%i3) cflength: 1$

(%i4) cf ((1 + sqrt(5))/2);
(%o4)                           [1, 1, 1, 1, 2]
(%i5) cflength: 2$

(%i6) cf ((1 + sqrt(5))/2);
(%o6)                      [1, 1, 1, 1, 1, 1, 1, 2]
(%i7) cflength: 3$

(%i8) cf ((1 + sqrt(5))/2);
(%o8)                  [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]

A continued fraction can be evaluated by evaluating the arithmetic representation returned by cfdisrep.

(%i9) cflength: 3$

(%i10) cfdisrep (cf (sqrt (3)))$

(%i11) ev (%, numer);
(%o11)                         1.73170731707317

Maxima does not know about operations on continued fractions outside of cf.

(%i12) cf ([1,1,1,1,1,2] * 3);
(%o12)                           [4, 1, 5, 2]
(%i13) cf ([1,1,1,1,1,2]) * 3;
(%o13)                        [3, 3, 3, 3, 3, 6]

cit. & loll – 130

Arriva cit.osa e lollosa come sempre 😋

000decreto-carige

Reminder: We used to think about it as the far distant future. Starting tomorrow only 20 years are left
::: okasion2012

may you be ashamed of the code you wrote in 2018, because it means that you learned something and improved your coding skills
::: mariofusco

Happy New Year! If you’re still working on your 2019 resolutions, don’t only plan what you want to do, but also plan what you want to learn. This may be the best investment you can make in your future. I regularly set learning goals for myself, and hope you will too!
::: AndrewYNg

E’ pur sempre debugging
::: andreacolangelo

Ça commence à faire beaucoup de coïncidences. 🤔
::: Bouletcorp

Best 404 page ever! 😂
::: DZone

Hello, I just wanted you to know that I had sushi
::: vikkio88

Recognise genuinely smart people
::: RichRogersIoT

I was bitching about time in operating systems when I came across this 1857 time table
::: cpuGoogle

UBC is now the #1 Canadian University for PL.*
::: wilbowma

The third highest-rated professor at Harvard is “Stack Overflow”
vero o loll? CMQ dr. Overflow è sempre disponibile, anche per quelli di fuori
::: MIT_CSAIL

dwn7x9tuuaehxho

Sequencing (e.g., the semicolon, BEGIN, PROGN, Python newline, …) is a brittle and terribly weak abstraction. It’s an overused bug magnet
::: stylewarning

ero curiosa di vedere se il profilo incluso fosse davvero quello del Ministero della Difesa
::: terminologia

In case you were wondering who will control all the machines…
::: evgenymorozov

distante “ben 27 mila km”
::: cmnit

Pearls Before Swine for January 05, 2019
::: _juhan

When someone uses spaces over tabs
::: dvIpr

Holy crap I’m a professor!
l’entusiasmo dei nuovi 😁 lovevole ❤️
::: wilbowma ::: wilbowma

WTF?
::: TheKenMunroShow

Computer Science Courses that Don’t Exist, But Should
::: RichRogersIoT

So many very good robots!
::: mikamckinnon

dwdgtj8w0au3efi

Nell mi vit ho comprto due tstiere @Logitech
::: ivosilvestro

il terziario che ci piace
::: lautonini

Starship test vehicle under assembly will look similar to this illustration when finished. Operational Starships would obv have windows, etc.
::: elonmusk

Remember: Every time you misidentify a traffic light in a Captcha
::: libovness

Hey technologies, please stop
::: coolstuffcheap

Every great developer you know got there by solving problems they were unqualified
::: CodeWisdom

I’m ready for the meteor of death now
::: AlexKoppelman

having too many tabs open is an age-old problem
::: sarayasin

Heathrow departures stopped as drone reported
::: BBCNews

lty_dnfu

Componenti buoni si vedono
::: pri_mario

Working with an unplugged laptop
::: ktf

Se la conoscenza può creare dei problemi
::: miracolosegreto

As a first approximation
::: Dereklowe

Gosh, these old professors, making me use ancient technology like Java
::: wilbowma

Question (s)
::: jk_rowling

*closing 20 browser tabs* you do not spark joy
::: ReinH

#Javascript syntax of functional methods like filter and map feels very kludgy
::: Gianlucadfiore

La precisione degli orologiai sarebbe inutile
::: LorenzoTomasin

Ho fatto incazzare una strega in chat
::: Dio

john kraus

John Kraus

The indispensable function of the mathematician
::: JohnDCook

Ma quelli che nella bio scrivono “influencer” e non arrivano a mille followers…
::: BeppeBeppetti

Boomers: When life hands you lemons, make lemonade
::: HydroHaacker

Inventor of USB Unintentionally
::: HardDriveMag

Un racconto di fantascienza in un tweet
::: disinformatico

been reading about sequences that converge to zero. they’re so cool
::: cwillmore

Oh this is the secret o getting tenure?!
::: wilbowma

This was the best two minutes of my life
::: bedroomflicker

TIL that changing random stuff until your program works is “hacky” and “bad coding practice”
::: smaine

8 y.o. reading “Girls who code”
::: elibendersky

that-s-all

Maxima – 168 – Somme, prodotti e serie – 5

dtsf

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.509.

Serie di Fourier

The fourie package comprises functions for the symbolic computation of Fourier series. There are functions in the fourie package to calculate Fourier integral coefficients and some functions for manipulation of expressions.

Nota: senza la “r“.

equalp (x, y)
Returns true if equal (x, y) otherwise false (doesn’t give an error message like equal (x, y) would do in this case).

remfun (f, expr)
remfun (f, expr, x)
remfun (f, expr) replaces all occurrences of f (arg) by arg in expr.

remfun (f, expr, x) replaces all occurrences of f (arg) by arg in expr only if arg contains the variable x.

funp (f, expr)
funp (f, expr, x)
funp (f, expr) returns true if expr contains the function f.

funp (f, expr, x) returns true if expr contains the function f and the variable x is somewhere in the argument of one of the instances of f.

absint (f, x, halfplane)
absint (f, x)
absint (f, x, a, b)
absint (f, x, halfplane) returns the indefinite integral of f with respect to x in the given halfplane (pos, neg, or both). f may contain expressions of the form abs (x), abs (sin (x)), abs (a) * exp (-abs (b) * abs (x)).

absint (f, x) is equivalent to absint (f, x, pos).

absint (f, x, a, b) returns the definite integral of f with respect to x from a to b. f may include absolute values.

fourier (f, x, p)
Returns a list of the Fourier coefficients of f(x) defined on the interval [-p, p].

foursimp (l)
Simplifies sin (n %pi) to 0 if sinnpiflag is true and cos (n %pi) to (-1)^n if cosnpiflag is true.

sinnpiflag
Default value: true. See foursimp.

cosnpiflag
Default value: true. See foursimp.

fourexpand (l, x, p, limit)
Constructs and returns the Fourier series from the list of Fourier coefficients l up through limit terms (limit may be inf). x and p have same meaning as in fourier.

fourcos (f, x, p)
Returns the Fourier cosine coefficients for f(x) defined on [0, p].

foursin (f, x, p)
Returns the Fourier sine coefficients for f(x) defined on [0, p].

totalfourier (f, x, p)
Returns fourexpand (foursimp (fourier (f, x, p)), x, p, 'inf).

fourint (f, x)
Constructs and returns a list of the Fourier integral coefficients of f(x) defined on [minf, inf].

fourintcos (f, x)
Returns the Fourier cosine integral coefficients for f(x) on [0, inf].

fourintsin (f, x)
Returns the Fourier sine integral coefficients for f(x) on [0, inf].

Funzioni e variabili per la serie di Poisson

intopois (a)
Converts a into a Poisson encoding.

outofpois (a)
Converts a from Poisson encoding to general representation. If a is not in Poisson form, outofpois carries out the conversion, i.e., the return value is outofpois (intopois (a)). This function is thus a canonical simplifier for sums of powers of sine and cosine terms of a particular type.

poisdiff (a, b)
Differentiates a with respect to b. b must occur only in the trig arguments or only in the coefficients.

poisexpt (a, b)
Functionally identical to intopois (a^b). b must be a positive integer.

poisint (a, b)
Integrates in a similarly restricted sense (to poisdiff). Non-periodic terms in b are dropped if b is in the trig arguments.

poislim
Default value: 5.

poislim determines the domain of the coefficients in the arguments of the trig functions. The initial value of 5 corresponds to the interval [-2^(5-1)+1,2^(5-1)], or [-15,16], but it can be set to [-2^(n-1)+1, 2^(n-1)].

poismap (series, sinfn, cosfn)
will map the functions sinfn on the sine terms and cosfn on the cosine terms of the Poisson series given. sinfn and cosfn are functions of two arguments which are a coefficient and a trigonometric part of a term in series respectively.

poisplus (a, b)
Is functionally identical to intopois (a + b).

poissimp (a)
Converts a into a Poisson series for a in general representation.

poisson
The symbol /P/ follows the line label of Poisson series expressions.

poissubst (a, b, c)
Substitutes a forb in c. c is a Poisson series.

(1) Where b is a variable u, v, w, x, y, or z, then a must be an expression linear in those variables (e.g., 6*u + 4*v).

(2) Where b is other than those variables, then a must also be free of those variables, and furthermore, free of sines or cosines.

poissubst (a, b, c, d, n) is a special type of substitution which operates on a and b as in type (1) above, but where d is a Poisson series, expands cos(d) and sin(d) to order n so as to provide the result of substituting a + d for b in c. The idea is that d is an expansion in terms of a small parameter. For example, poissubst (u, v, cos(v), %e, 3) yields cos(u)*(1 - %e^2/2) - sin(u)*(%e - %e^3/6).

poistimes (a, b)
Is functionally identical to intopois (a*b).

poistrim ()
is a reserved function name which (if the user has defined it) gets applied during Poisson multiplication. It is a predicate function of 6 arguments which are the coefficients of the u, v, ..., z in a term. Terms for which poistrim is true (for the coefficients of that term) are eliminated during multiplication.

printpois (a)
Prints a Poisson series in a readable format. In common with outofpois, it will convert a into a Poisson encoding first, if necessary.

Maxima – 167 – Somme, prodotti e serie – 4

petsciibots-5

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.504.

taylor (expr, x, a, n)
taylor (expr, [x_1, x_2, ...], a, n)
taylor (expr, [x, a, n, 'asymp])
taylor (expr, [x_1, x_2, ...], [a_1, a_2, ...], [n_1, n_2, ...])
taylor (expr, [x_1, a_1, n_1], [x_2, a_2, n_2], ...)
taylor (expr, x, a, n) expands the expression expr in a truncated Taylor or Laurent series in the variable x around the point a, containing terms through (x - a)^n.

If expr is of the form f(x)/g(x) and g(x) has no terms up to degree n then taylor attempts to expand g(x) up to degree 2 n. If there are still no nonzero terms, taylor doubles the degree of the expansion of g(x) so long as the degree of the expansion is less than or equal to n 2^taylordepth.

taylor (expr, [x_1, x_2, ...], a, n) returns a truncated power series of degree n in all variables x_1, x_2, ... about the point (a, a, ...).

taylor (expr, [x_1, a_1, n_1], [x_2, a_2, n_2], ...) returns a truncated power series in the variables x_1, x_2, ... about the point (a_1, a_2, ...), truncated at n_1, n_2, ....

taylor (expr, [x_1, x_2, ...], [a_1, a_2, ...], [n_1, n_2, ...]) returns a truncated power series in the variables x_1, x_2, ... about the point (a_1, a_2, ...), truncated at n_1, n_2, ....

taylor (expr, [x, a, n, 'asymp]) returns an expansion of expr in negative powers of x - a. The highest order term is (x - a)^-n.

When maxtayorder is true, then during algebraic manipulation of (truncated) Taylor series, taylor tries to retain as many terms as are known to be correct.

When psexpand is true, an extended rational function expression is displayed fully expanded. The switch ratexpand has the same effect. When psexpand is false, a multivariate expression is displayed just as in the rational function package. When psexpand is multi, then terms with the same total degree in the variables are grouped together.

See also the taylor_logexpand switch for controlling expansion.

(%i1) taylor (sqrt (sin(x) + a*x + 1), x, 0, 3);
                           2             2       3      2             3
             (a + 1) x   (a  + 2 a + 1) x    (3 a  + 9 a  + 9 a - 1) x
(%o1)/T/ 1 + --------- - ----------------- + -------------------------- + . . .
                 2               8                       48
(%i2) %^2;
                                           3
                                          x
(%o2)/T/                  1 + (a + 1) x - -- + . . .
                                          6
(%i3) taylor (sqrt (x + 1), x, 0, 5);
                              2    3      4      5
                         x   x    x    5 x    7 x
(%o3)/T/             1 + - - -- + -- - ---- + ---- + . . .
                         2   8    16   128    256
(%i4) %^2;
(%o4)/T/                         1 + x + . . .
(%i5) product ((1 + x^i)^2.5, i, 1, inf)/(1 + x^2);
                                inf
                               /===\
                                ! !    i     2.5
                                ! !  (x  + 1)
                                ! !
                               i = 1
(%o5)                          -----------------
                                     2
                                    x  + 1
(%i6) ev (taylor(%, x, 0, 3), keepfloat);
                                      2           3
(%o6)/T/           1 + 2.5 x + 3.375 x  + 6.5625 x  + . . .
(%i7) taylor (1/log (x + 1), x, 0, 3);
                                      2       3
                        1   1   x    x    19 x
(%o7)/T/                - + - - -- + -- - ----- + . . .
                        x   2   12   24    720
(%i8) taylor (cos(x) - sec(x), x, 0, 5);
                                        4
                                  2    x
(%o8)/T/                      (- x ) - -- + . . .
                                       6
(%i9) taylor ((cos(x) - sec(x))^3, x, 0, 5);
(%o9)/T/                           0 + . . .
(%i10) taylor (1/(cos(x) - sec(x))^3, x, 0, 5);
                                                 2          4
             1      1       11      347    6767 x    15377 x
(%o10)/T/ (- --) + ---- + ------ - ----- - ------- - -------- + . . .
              6       4        2   15120   604800    7983360
             x     2 x    120 x
(%i11) taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6);
               2  2       4      2   4        6       4       2   6
              k  x    (3 k  - 4 k ) x    (45 k  - 60 k  + 16 k ) x
(%o11)/T/ 1 - ----- - ---------------- - -------------------------- + . . .
                2            24                     720
(%i12) taylor ((x + 1)^n, x, 0, 4);
                      2       2     3      2         3
                    (n  - n) x    (n  - 3 n  + 2 n) x
(%o12)/T/ 1 + n x + ----------- + --------------------
                         2                 6
                                             4      3       2         4
                                           (n  - 6 n  + 11 n  - 6 n) x
                                         + ---------------------------- + . . .
                                                        24
(%i13) taylor (sin (y + x), x, 0, 3, y, 0, 3);
               3                       2                        3
              y                       y                   y    y            2
(%o13)/T/ ((- --) + y + . . .) + (1 - -- + . . .) x + ((- -) + -- + . . .) x
              6                       2                   2    12
                                                          2
                                                    1    y            3
                                              + ((- -) + -- + . . .) x  + . . .
                                                    6    12
(%i14) taylor (sin (y + x), [x, y], 0, 3);
                             3        2      2      3
                            x  + 3 y x  + 3 y  x + y
(%o14)/T/         (y + x) - ------------------------- + . . .
                                        6
(%i15) taylor (1/sin (y + x), x, 0, 3, y, 0, 3);
           y   1                1     1               1            2
(%o15)/T/ (- + - + . . .) + ((- --) + - + . . .) x + (-- + . . .) x
           6   y                 2    6                3
                                y                     y
                                                        1             3
                                                  + ((- --) + . . .) x  + . . .
                                                         4
                                                        y
(%i16) taylor (1/sin (y + x), [x, y], 0, 3);
                               3         2       2        3
              1     x + y   7 x  + 21 y x  + 21 y  x + 7 y
(%o16)/T/   ----- + ----- + ------------------------------- + . . .
            x + y     6                   360

taylordepth
Default value: 3.

If there are still no nonzero terms, taylor doubles the degree of the expansion of g(x) so long as the degree of the expansion is less than or equal to n 2^taylordepth.

taylorinfo (expr)
Returns information about the Taylor series expr. The return value is a list of lists. Each list comprises the name of a variable, the point of expansion, and the degree of the expansion.

taylorinfo returns false if expr is not a Taylor series.

(%i1) taylor ((1 - y^2)/(1 - x), x, 0, 3, [y, a, inf]);
                2                         2
(%o1)/T/ ((1 - a ) - 2 a (y - a) - (y - a) )
              2                        2
 + ((- (y - a) ) - 2 a (y - a) + (1 - a )) x
              2                        2    2
 + ((- (y - a) ) - 2 a (y - a) + (1 - a )) x
              2                        2    3
 + ((- (y - a) ) - 2 a (y - a) + (1 - a )) x  + . . .
(%i2) taylorinfo(%);
(%o2)                      [[x, 0, 3], [y, a, inf]]

taylorp (expr)
Returns true if expr is a Taylor series, and false otherwise.

taylor_logexpand
Default value: true.

taylor_logexpand controls expansions of logarithms in taylor series.

When taylor_logexpand is true, all logarithms are expanded fully so that zero-recognition problems involving logarithmic identities do not disturb the expansion process. However, this scheme is not always mathematically correct since it ignores branch information.

When taylor_logexpand is set to false, then the only expansion of logarithms that occur is that necessary to obtain a formal power series.

taylor_order_coefficients
Default value: true.

taylor_order_coefficients controls the ordering of coefficients in a Taylor series.

When taylor_order_coefficients is true, coefficients of taylor series are ordered canonically.

taylor_simplifier (expr)
Simplifies coefficients of the power series expr. taylor calls this function.

taylor_truncate_polynomials
Default value: true.

When taylor_truncate_polynomials is true, polynomials are truncated based upon the input truncation levels.

Otherwise, polynomials input to taylor are considered to have infinite precison.

taytorat (expr)
Converts expr from taylor form to canonical rational expression (CRE) form. The effect is the same as rat (ratdisrep (expr)), but faster.

trunc (expr)
Annotates the internal representation of the general expression expr so that it is displayed as if its sums were truncated Taylor series. expr is not otherwise modified.

(%i3) expr: x^2 + x + 1;
                                   2
(%o3)                             x  + x + 1
(%i4) trunc (expr);
                                       2
(%o4)                         1 + x + x  + . . .
(%i5) is (expr = trunc (expr));
(%o5)                                true

unsum (f, n)
Returns the first backward difference f(n) - f(n - 1). Thus unsum in a sense is the inverse of sum. See also nusum.

(%i6) g(p) := p*4^n/binomial(2*n,n);
                                            n
                                         p 4
(%o6)                      g(p) := ----------------
                                   binomial(2 n, n)
(%i7) g(n^4);
                                     4  n
                                    n  4
(%o7)                          ----------------
                               binomial(2 n, n)
(%i8) nusum (%, n, 0, n);
                           4        3       2              n
            2 (n + 1) (63 n  + 112 n  + 18 n  - 22 n + 3) 4     2
(%o8)       ------------------------------------------------ - ---
                          693 binomial(2 n, n)                 231
(%i9) unsum (%, n);
                                     4  n
                                    n  4
(%o9)                          ----------------
                               binomial(2 n, n)

verbose
Default value: false.

When verbose is true, powerseries prints progress messages.

Sicurezza e disinformazione – 6

La solita rassegna –quasi: ieri ho postato una serie sbagliata, oggi continuo 😋

000475x255_1532866644759.rainews_20180729141644994

New surveillance practices continued to erode the privacy of people in Latin America. Yet local digital rights organizations, journalists, security researchers and local activists are working tirelessly to fight back
privacy, sicurezza, spionaggio, virus
::: EFF

Why Huawei Gives the US and Its Allies Security Nightmares
privacy, sicurezza, spionaggio, virus
::: Slashdot

I never tire of looking at videos of Chinese click farms. It’s just so surreal to see hundreds of phones playing the same video for the purposes of fake engagment
disinformazione, fake news, bufale
::: mbrennanchina

Always online meets AI and that means no data, and no person, is truly anonymous, at least not for long
artificial intelligence
::: Kasparov63

There is nothing in the political journalism playbook for what to do when the presidency becomes the most potent force in the culture for dis- and mis-informing the American public. For one thing, it destroys the logic of “access”
disinformazione, fake news, bufale
::: jayrosen_nyu

My unpopular 2019 prediction: attacks on large scale cloud providers, and maybe not using speculative execution, but vulnerabilities in the architecture and orchestrators themselves
privacy, sicurezza, spionaggio, virus
::: jessfraz

First-Ever UEFI Rootkit Tied To Sednit APT
privacy, sicurezza, spionaggio, virus
::: Slashdot

Democratic Republic of Congo internet shutdown shows how Chinese censorship tactics are spreading
a senior adviser to DRC President Joseph Kabila, said internet and text messaging services were shut down to preserve public order after “fictitious results” were circulated on social media
censura
::: fabiochiusi

Thread👇 – in the disinformation landscape, it’s important to trace the origin of information and how it makes its way to “reputable” outlets. Disinformation often starts as “sketchy” news on fringe websites, and gradually gains credibility by being posted by reputable sources
disinformazione, fake news, bufale
::: gianluca_string

Solid free guide on how to do secure product devlopment. Free, too. Published by the National Cyber Security Centre Finland aka Kyberturvallisuuskeskus (but don’t worry, the booklet is in English)
privacy, sicurezza, spionaggio, virus | manuali, how to
::: mikko

Sudan has blocked Facebook, Twitter and Instagram to counter anti-govt protests
censura
::: fabiochiusi

dwn_kmgwoaeos4j

USB Type-C Authentication Program Launched
privacy, sicurezza, spionaggio, virus
::: Slashdot

Iran Extends Social Media Crackdown With Move To Bar Instagram
censura
::: Slashdot

Interesting look into China’s censorship factories — a model many in the West would love to replicate
censura
::: fabiochiusi

One year ago today security experts announced the #Spectre and #Meltdown vulnerabilities in #Intel processors. Here’s how they happened – and how they could’ve been prevented
hardware | bug
::: MIT_CSAIL ::: Slashdot

Microsoft is Privately Testing ‘Bali,’ a Way To Give Users Control of Data Collected About Them
dati, raccolta
::: Slashdot

Automatic Equivalence Checking for Assembly Implementations of Cryptography Libraries
privacy, sicurezza, spionaggio, virus
::: johnregehr

Fake news succeeds when it reinforces existing prejudices, and that goes for the prestigious Der Spiegel, not just social media memes
disinformazione, fake news, bufale
::: Kasparov63

The Lies Comcast Allegedly Told Customers To Hide Full Cost of Service
frodi
::: Slashdot

The Cyberspace Administration of China on Thursday announced it was starting a six-month effort to eradicate “vulgar” information” from a plethora of online media, including messaging services and livestreaming platforms
define vulgar
censura
::: fabiochiusi

Internet services down, broadcasters blocked, journalist expelled. DRC’s minister of communication Lambert Mende said “cutting the signal of some media is the duty of the government” reports @mediacongo
censura
::: IFEX

alarm

Pagnoncelli sostiene ci sia una differenza enorme di percezione delle priorità da affrontare tra livello nazionale (immigrazione 37%, ambiente 8%) e locale (immigrazione 13%, ambiente 30%). Un dato interessante per capire il rapporto tra propaganda e realtà
media
::: fabiochiusi

Per @Repubblica, sulla Luna ci sono “aree piatte da abbattere”. Giornalismo fatto con Google Translate usato a neuroni spenti
media
::: disinformatico

This is an amazing piece. To censor China’s internet, the censors have to be taught the real version of Chinese history so that they know what to block
censura
::: Birdyword

“Much of the news currently published online is simply not worth paying for. Some of it is hardly worth our fleeting attention, let alone hard-earned cash.” Building a new business of news is necessary and requires fundamental change led by journalists
media
::: rasmus_kleis

Hackers Dump Data on Merkel, Hundreds of German Politicians
It’s the biggest data dump of its kind in Germany
privacy, sicurezza, spionaggio, virus
::: business ::: fabiochiusi

Google is quietly infiltrating medicine — but what rules will it play by?
privacy, sicurezza, spionaggio, virus
::: angelasimone

Security Researcher Cracks Google’s Widevine DRM (L3 Only)
privacy, sicurezza, spionaggio, virus
::: Slashdot

The exponential increase in the collection and analysis of information by government and private actors has attracted critique regarding ‘bad #data’ practices. A new book proposes a move from critique to imagining an optimistic vision of a datafied future
dati, raccolta
::: GianlucaSgueo

A vision of the dark future of advertising
dati, raccolta
::: journalismfest

YouTube’s Biggest Stars Are Pushing a Shady Polish Gambling Site
privacy, sicurezza, spionaggio, virus
::: Slashdot

168050b8

Integrity Initiative: 4th release of documents available to download – separately or in a folder. A lot to go through here. Many countries. More on the Skripals story. Could be a busy weekend…
CyberGuerrilla: British informational war against all
Web, Internet | dati, raccolta
::: Tim_Hayward_

Must-read essay on what privacy means and why it matters
privacy, sicurezza, spionaggio, virus
::: jeanqasaur

Excellent piece on why privacy has become a threat on par with security in 2018. Glad to be working in this space!
privacy, sicurezza, spionaggio, virus
::: AkitaSoftware

First book I’ve read this year is The Age of Surveillance Capitalism by Shoshana Zuboff. Will be hard to find a more thought-provoking book to read in the rest of the year
privacy, sicurezza, spionaggio, virus
::: johnthornhillft

Google Drive Has a Serious Spam Problem, But Google Says a Fix is Coming
spam
::: Slashdot

Internet shutdowns have spiked sharply around the world in recent years, rising from 75 in 2016 to almost 190 last year
censura
::: fabiochiusi

DuckDuckGo Denies Using Fingerprinting To Track Its Users
privacy, sicurezza, spionaggio, virus
::: Slashdot

Here’s a good article for the people asking me if data anonymization techniques work in preserving anonymity. Tl;dr: no, especially not when you can link different data sets together
privacy, sicurezza, spionaggio, virus
::: jeanqasaur

Companies Are Now Offering Seven Figures For Hacks That Allow Spies, Cops To Steal Chat App Messages
privacy, sicurezza, spionaggio, virus
::: Slashdot

LinkedIn Censored Another Critic Of The Chinese Government
censura
::: JohnPaczkowski

power

Maxima – 166 – Somme, prodotti e serie – 3

jkop

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.501.

pade (taylor_series, numer_deg_bound, denom_deg_bound)
Returns a list of all rational functions which have the given Taylor series expansion where the sum of the degrees of the numerator and the denominator is less than or equal to the truncation level of the power series, i.e. are “best” approximants, and which additionally satisfy the specified degree bounds.

taylor_series is a univariate Taylor series. numer_deg_bound and denom_deg_bound are positive integers specifying degree bounds on the numerator and denominator.

taylor_series can also be a Laurent series, and the degree bounds can be inf which causes all rational functions whose total degree is less than or equal to the length of the power series to be returned. Total degree is defined as numer_deg_bound + denom_deg_bound. Length of a power series is defined as "truncation level" + 1 - min(0, "order of series").

(%i1) taylor (1 + x + x^2 + x^3, x, 0, 3);
                                     2    3
(%o1)/T/                    1 + x + x  + x  + . . .
(%i2) pade (%, 1, 1);
                                        1
(%o2)                              [- -----]
                                      x - 1
(%i3) t: taylor(-(83787*x^10 - 45552*x^9 - 187296*x^8
                  + 387072*x^7 + 86016*x^6 - 1507328*x^5
                  + 1966080*x^4 + 4194304*x^3 - 25165824*x^2
                  + 67108864*x - 134217728)
         /134217728, x, 0, 10);
                    2    3       4       5       6        7         8         9
             x   3 x    x    15 x    23 x    21 x    189 x    5853 x    2847 x
(%o3)/T/ 1 - - + ---- - -- - ----- + ----- - ----- - ------ + ------- + -------
             2    16    32   1024    2048    32768   65536    4194304   8388608
                                                                     10
                                                              83787 x
                                                            - --------- + . . .
                                                              134217728
(%i4) pade (t, 4, 4);
(%o4)                                 []

There is no rational function of degree 4 numerator/denominator, with this power series expansion. You must in general have degree of the numerator and degree of the denominator adding up to at least the degree of the power series, in order to have enough unknown coefficients to solve.

(%i5) pade (t, 5, 5);
                     5                4                 3                  2
(%o5) [- (520256329 x  - 96719020632 x  - 489651410240 x  - 1619100813312 x
                                                  5                 4
 - 2176885157888 x - 2386516803584)/(47041365435 x  + 381702613848 x
                  3                  2
 + 1360678489152 x  + 2856700692480 x  + 3370143559680 x + 2386516803584)]

powerseries (expr, x, a)
Returns the general form of the power series expansion for expr in the variable x about the point a (which may be inf for infinity):

           inf
           ====
           \               n
            >    b  (x - a)
           /      n
           ====
           n = 0

If powerseries is unable to expand expr, taylor may give the first several terms of the series.

When verbose is true, powerseries prints progress messages.

(%i6) verbose: true$

(%i7) powerseries (log(sin(x)/x), x, 0);
trigreduce: failed to expand.

                                      sin(x)
                                  log(------)
                                        x

trigreduce: try again after applying rule:
                                        d   sin(x)
                                      / -- (------)
                            sin(x)    [ dx    x
                        log(------) = I ----------- dx
                              x       ]   sin(x)
                                      /   ------
                                            x


powerseries: first simplification returned
        x
       /
       [  csc(g19154) sin(g19154) - g19154 cos(g19154) csc(g19154)
     - I  -------------------------------------------------------- dg19154
       ]                           g19154
       /
        0


powerseries: first simplification returned
                             g19154 cot(g19154) - 1
                           - ----------------------
                                     g19154

powerseries: attempt rational function expansion of
                                      1
                                    ------
                                    g19154
                   inf
                   ====        i2  2 i2 - 1             2 i2
                   \      (- 1)   2         bern(2 i2) x
(%o7)               >     ----------------------------------
                   /                  i2 (2 i2)!
                   ====
                   i2 = 1

La reference da un’espressione finale diversa 😐

psexpand
Default value: false.

When psexpand is true, an extended rational function expression is displayed fully expanded. The switch ratexpand has the same effect.

When psexpand is false, a multivariate expression is displayed just as in the rational function package.

When psexpand is multi, then terms with the same total degree in the variables are grouped together.

revert (expr, x)
revert2 (expr, x, n)
These functions return the reversion of expr, a Taylor series about zero in the variable x. revert returns a polynomial of degree equal to the highest power in expr. revert2 returns a polynomial of degree n, which may be greater than, equal to, or less than the degree of expr.

load ("revert") loads these functions.

(%i1) load ("revert")$

(%i2) t: taylor (exp(x) - 1, x, 0, 6);
                          2    3    4    5     6
                         x    x    x    x     x
(%o2)/T/             x + -- + -- + -- + --- + --- + . . .
                         2    6    24   120   720
(%i3) revert (t, x);
                      6       5       4       3       2
                  10 x  - 12 x  + 15 x  - 20 x  + 30 x  - 60 x
(%o3)/R/        - --------------------------------------------
                                       60
(%i4) ratexpand (%);
                            6     5    4    3    2
                           x     x    x    x    x
(%o4)                   (- --) + -- - -- + -- - -- + x
                           6     5    4    3    2
(%i5) taylor (log(x+1), x, 0, 6);
                           2    3    4    5    6
                          x    x    x    x    x
(%o5)/T/              x - -- + -- - -- + -- - -- + . . .
                          2    3    4    5    6
(%i6) ratsimp (revert (t, x) - taylor (log(x+1), x, 0, 6));
(%o6)                                  0
(%i7) revert2 (t, x, 4);
                                 4     3    2
                                x     x    x
(%o7)                        (- --) + -- - -- + x
                                4     3    2

AI, innovazioni e blockchain – 56

OK la rassegna delle novità innovative che ritorna al martedì.

dwpxofyw0aiik-m

1/The rise of Software Engineering required inventing processes like version control, code review, agile, to help teams work effectively. The rise of AI & Machine Learning Engineering is now requiring new processes, like how we split train/dev/test, model zoos, etc.
thread lungo
artificial intelligence | machine learning
::: AndrewYNg

Chang’e-4 è arrivata sulla faccia lontana della Luna: è la prima volta che una sonda arriva da quelle parti. Inoltre, si tratta di una missione abbastanza interessante e in questo articolo vi racconto perché
innovazioni, futuro
::: quantizzando

Genetically modified ‘shortcut’ boosts plant growth by 40%. However, the authors recognise that using genetic modification is controversial in many parts of the world
innovazioni, futuro
::: hronir

What Tech Will Look Like in 2039
tecnologia
::: medialab

Cómo Barcelona se convirtió en la smart city más revolucionaria del mundo (una partecita de Los dueños de internet, con entrevista a @subirats9 y mención al trabajo de @AdaColau y @francesca_bria)
innovazioni, futuro
::: nataliazuazo ::: lauratraldi

Texas Has Enough Sun and Wind To Quit Coal, Rice Researchers Say
innovazioni, futuro
::: Slashdot

A new generation of environmentalists is embracing our country’s number one source of #cleanenergy– nuclear energy. Why more are advocating for nuclear as critical in reducing our carbon emissions and preserving our planet
innovazioni, futuro
::: NEI

What Happens When the Rich Live Decades Longer Than the Rest of Us?
tecnologia
::: waltmossberg

White House Advisor Kudlow Says Apple Technology May Have Been ‘Picked Off’ by China
tecnologia
::: Slashdot

The wall that once separated Information Technology from Operational Technology has come crashing down.There is now a huge demand for workers who can move easily between the world of computers & the world of machines
economia, lavoro
::: RichRogersIoT

Miners Say They Dig AI But the Gold Rush Hasn’t Come
artificial intelligence
::: Slashdot

dwoh4lxxcauloka

This year Audi says it’ll be the first company in the world to sell a Level 3 car directly to the public
automazione
::: IEEESpectrum

Implementing a Natural Language Classifier in iOS with Keras + Core ML
machine learning
::: fchollet

Amazon Says 100 Million Alexa Devices Have Been Sold
hardware
::: Slashdot

German power generation passed 40% renewable share for the first time last year! When I was young, we were told that at most 3% renewable share is possible…
innovazioni, futuro
::: rahmstorf

Because progress is about disrupting laziness
robots
::: fabiochiusi

Un’auto elettrica con 220 km di autonomia realistica a circa 15.000 euro (anche meno con i sussidi). In Cina succede
innovazioni, futuro
::: disinformatico

Boston Dynamics has done it again
robots
::: DigitalTrends

China To Launch Self-Driving Bullet Trains That Will Travel At 217 MPH
automazione
::: Slashdot

This by @POLITICOEurope is a great story on how to really democratize AI: teach it, at every level — but starting from those who know nothing of it. Knowledge is a competitive advantage, even in the AI era
artificial intelligence
::: fabiochiusi

The ability of AI to intrude upon – and potentially control – private human behaviour has direct implications for the UN’s human rights agenda
artificial intelligence
::: MarietjeSchaake

dwugxwpwsaahytm

“As US oil output surges, companies are burning the gas they cannot squeeze onto pipelines”. An exemplar of what the UN Secretary-General calls “immoral” and “suicidal” behaviour. And all fueled by a growing debt bubble to boot
economia, lavoro
::: JeremyLeggett

The powerful and lucrative alliance between AI and a data-driven society has made social networks the architects of our exchanges, the new masters reshaping the very fabric of reality.
artificial intelligence
::: FrankPasquale

Even More Americans Have Stopped Biking To Work
economia, lavoro
::: Slashdot

Swarm wants to create an orbital network of miniature satellites that will offer a global Internet of Things communication service at a fraction of the price of existing systems
Web, Internet
::: IEEESpectrum

GM and DoorDash Announce Self-Driving Cars Delivering Food In San Francisco
automazione
::: Slashdot

I work in the FiDi in San Francisco and live 40 miles away, on the hills above Stanford. I’ve spent a lot of time trying to engineer my commute in order to not be one of those people spending two hours per day in a single-occupancy car, unable to read or work. I failed
economia, lavoro
::: Paradosso

Here is an end-to-end canonical sample for training a model on Cloud TPUs in Keras. It has full code for loading the data from scratch using http://tf.data .Dataset and also exporting the trained model to ML Engine for inference
machine learning
::: martin_gorner

Gennaio 2018
blockchain e crypto*
::: BTC_PRICE

Anti-Tesla Pickup Truck Drivers Take Over a Supercharger Station — Again
innovazioni, futuro
::: Slashdot

dwknsbbu0aambfg

Ars Technica’s 2019 ‘Deathwatch’ List Includes Essential and ‘Facebook Management’
economia, lavoro
::: Slashdot

The new #geopolitics of artificial intelligence
artificial intelligence
::: wef

Nine charts that really bring home just how fast AI is growing. Artificial intelligence is booming in Europe, China, and the US, but it’s still a very male industry
artificial intelligence
::: medialab

Robotics is so far forward with the controls, with the sensors, with the AI. What’s holding it back is actuation
robots | artificial intelligence
::: IEEESpectrum

There are 43 million mobile phones and fewer than 70,000 landlines in Kenya. This year, Alphabet subsidiary Loon will provide its first commercial cellular service to residents there from balloons overhead
Web, Internet
::: IEEESpectrum

What can you expect from #CES2019? The rise of AI-driven vehicles, high hopes for #5G, and better personal medical devices, says one expert in this show preview
innovazioni, futuro
::: IEEESpectrum ::: IEEESpectrum

Apocalittici e integrati nell’epoca dell’intelligenza artificiale
artificial intelligence
::: lucadebiase

Elon Musk Breaks Ground on Tesla’s Shanghai Factory
innovazioni, futuro
::: Slashdot

New tutorial!🚀 Auto-Keras and AutoML: A Getting Started Guide
Python | machine learning
::: PyImageSearch

Recent Surveys on Graph Neural Networks
machine learning
::: ml_review

nope

Maxima – 165 – Somme, prodotti e serie – 2

dtj_1

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.497.

Funzioni e variabili per le serie

Maxima contains functions taylor and powerseries for finding the series of differentiable functions. It also has tools such as nusum capable of finding the closed form of some series. Operations such as addition and multiplication work as usual on series. This section presents the global variables which control the expansion.

cauchysum
Default value: false.

When multiplying together sums with inf as their upper limit, if sumexpand is true and cauchysum is true then the Cauchy product will be used rather than the usual product. In the Cauchy product the index of the inner summation is a function of the index of the outer one rather than varying independently.

(%i1) sumexpand: false$

(%i2) cauchysum: false$

(%i3) s: sum (f(i), i, 0, inf) * sum (g(j), j, 0, inf);
                             inf         inf
                             ====        ====
                             \           \
(%o3)                       ( >    f(i))  >    g(j)
                             /           /
                             ====        ====
                             i = 0       j = 0
(%i4) sumexpand: true$

(%i5) cauchysum: true$

(%i6) expand(s,0,0);
                        inf     i1
                        ====   ====
                        \      \
(%o6)                    >      >     g(i1 - i2) f(i2)
                        /      /
                        ====   ====
                        i1 = 0 i2 = 0

deftaylor (f_1 (x_1), expr_1, ..., f_n (x_n), expr_n)
For each function f_i of one variable x_i, deftaylor defines expr_i as the Taylor series about zero. expr_i is typically a polynomial in x_i or a summation; more general expressions are accepted by deftaylor without complaint.

powerseries (f_i(x_i), x_i, 0) returns the series defined by deftaylor.

deftaylor returns a list of the functions f_1, ..., f_n. deftaylor evaluates its arguments.

(%i1) deftaylor (f(x), x^2 + sum(x^i/(2^i*i!^2), i, 4, inf));
(%o1)                                 [f]
(%i2) powerseries (f(x), x, 0);
                             inf
                             ====      i1
                             \        x         2
(%o2)                         >     -------- + x
                             /       i1    2
                             ====   2   i1!
                             i1 = 4
(%i3) taylor (exp (sqrt (f(x))), x, 0, 4);
                             2         3          4
                            x    3073 x    12817 x
(%o3)/T/            1 + x + -- + ------- + -------- + . . .
                            2     18432     307200

maxtayorder
Default value: true.

When maxtayorder is true, then during algebraic manipulation of (truncated) Taylor series, taylor tries to retain as many terms as are known to be correct.

niceindices (expr)
Renames the indices of sums and products in expr. niceindices attempts to rename each index to the value of niceindicespref[1], unless that name appears in the summand or multiplicand, in which case niceindices tries the succeeding elements of niceindicespref in turn, until an unused variable is found. If the entire list is exhausted, additional indices are constructed by appending integers to the value of niceindicespref[1], e.g., i0, i1, i2, ....

niceindices returns an expression. niceindices evaluates its argument.

(%i1) niceindicespref;
(%o1)                         [i, j, k, l, m, n]
(%i2) product (sum (f (foo + i*j*bar), foo, 1, inf), bar, 1, inf);
                        inf    inf
                       /===\   ====
                        ! !    \
(%o2)                   ! !     >      f(bar i j + foo)
                        ! !    /
                       bar = 1 ====
                               foo = 1
(%i3) niceindices (%);
                            inf  inf
                           /===\ ====
                            ! !  \
(%o3)                       ! !   >    f(i j l + k)
                            ! !  /
                           l = 1 ====
                                 k = 1

niceindicespref
Default value: [i, j, k, l, m, n].

niceindicespref is the list from which niceindices takes the names of indices for sums and products.

The elements of niceindicespref are typically names of variables, although that is not enforced by niceindices.

(%i4) niceindicespref: [p, q, r, s, t, u]$

(%i5) product (sum (f (foo + i*j*bar), foo, 1, inf), bar, 1, inf);
                        inf    inf
                       /===\   ====
                        ! !    \
(%o5)                   ! !     >      f(bar i j + foo)
                        ! !    /
                       bar = 1 ====
                               foo = 1
(%i6) niceindices (%);
                            inf  inf
                           /===\ ====
                            ! !  \
(%o6)                       ! !   >    f(i j q + p)
                            ! !  /
                           q = 1 ====
                                 p = 1

nusum (expr, x, i_0, i_1)
Carries out indefinite hypergeometric summation of expr with respect to x using a decision procedure due to R.W. Gosper. expr and the result must be expressible as products of integer powers, factorials, binomials, and rational functions.

The terms “definite” and “indefinite summation” are used analogously to “definite” and “indefinite integration”. To sum indefinitely means to give a symbolic result for the sum over intervals of variable length, not just e.g. 0 to inf. Thus, since there is no formula for the general partial sum of the binomial series, nusum can’t do it.

nusum and unsum know a little about sums and differences of finite products. See also unsum.

(%i7) nusum (n*n!, n, 0, n);

solve: dependent equations eliminated: (1)
(%o7)                            (n + 1)! - 1
(%i8) nusum (n^4*4^n/binomial(2*n,n), n, 0, n);
                           4        3       2              n
            2 (n + 1) (63 n  + 112 n  + 18 n  - 22 n + 3) 4     2
(%o8)       ------------------------------------------------ - ---
                          693 binomial(2 n, n)                 231
(%i9) unsum (%, n);
                                     4  n
                                    n  4
(%o9)                          ----------------
                               binomial(2 n, n)
(%i10) unsum (prod (i^2, i, 1, n), n);
                           n - 1
                           /===\
                            ! !   2
(%o10)                    ( ! !  i ) (n - 1) (n + 1)
                            ! !
                           i = 1
(%i11) nusum (%, n, 1, n);

solve: dependent equations eliminated: (2 3)
                                   n
                                 /===\
                                  ! !   2
(%o11)                            ! !  i  - 1
                                  ! !
                                 i = 1

Maxima – 164 – Somme, prodotti e serie – 1

dtfn

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.493.

Funzioni e variabili per somme e prodotti

bashindices (expr)
Transforms the expression expr by giving each summation and product a unique index. This gives changevar greater precision when it is working with summations or products. The form of the unique index is jnumber. The quantity number is determined by referring to gensumnum, which can be changed by the user. For example, gensumnum:0$ resets it.

lsum (expr, x, L)
Represents the sum of expr for each element x in L. A noun form 'lsum is returned if the argument L does not evaluate to a list.

(%i1) lsum (x^i, i, [1, 2, 7]);
                                   7    2
(%o1)                             x  + x  + x
(%i2) lsum (i^2, i, rootsof (x^3 - 1, x));
                           ====
                           \      2
(%o2)                       >    i
                           /
                           ====
                                         3
                           i in rootsof(x  - 1, x)

intosum (expr)
Moves multiplicative factors outside a summation to inside. If the index is used in the outside expression, then the function tries to find a reasonable index, the same as it does for sumcontract. This is essentially the reverse idea of the outative property of summations, but note that it does not remove this property, it only bypasses it.

In some cases, a scanmap (multthru, expr) may be necessary before the intosum.

simpproduct
Default value: false.

When simpproduct is true, the result of a product is simplified. This simplification may sometimes be able to produce a closed form. If simpproduct is false or if the quoted form 'product is used, the value is a product noun form which is a representation of the pi notation used in mathematics.

product (expr, i, i_0, i_1)
Represents a product of the values of expr as the index i varies from i_0 to i_1. The noun form 'product is displayed as an uppercase letter pi.

product evaluates expr and lower and upper limits i_0 and i_1, product quotes (does not evaluate) the index i.

If the upper and lower limits differ by an integer, expr is evaluated for each value of the index i, and the result is an explicit product.

Otherwise, the range of the index is indefinite. Some rules are applied to simplify the product. When the global variable simpproduct is true, additional rules are applied.

In some cases, simplification yields a result which is not a product; otherwise, the
result is a noun form 'product.

See also nouns and evflag.

(%i3) product (x + i*(i+1)/2, i, 1, 4);
(%o3)                  (x + 1) (x + 3) (x + 6) (x + 10)
(%i4) product (i^2, i, 1, 7);
(%o4)                              25401600
(%i5) product (a[i], i, 1, 7);
(%o5)                        a  a  a  a  a  a  a
                              1  2  3  4  5  6  7
(%i6) product (a(i), i, 1, 7);
(%o6)                 a(1) a(2) a(3) a(4) a(5) a(6) a(7)
(%i7) product (a(i), i, 1, n);
                                    n
                                  /===\
                                   ! !
(%o7)                              ! !  a(i)
                                   ! !
                                  i = 1
(%i8) product (k, k, 1, n);
                                      n
                                    /===\
                                     ! !
(%o8)                                ! !  k
                                     ! !
                                    k = 1
(%i9) product (k, k, 1, n), simpproduct;
(%o9)                                 n!
(%i10) product (integrate (x^k, x, 0, 1), k, 1, n);
                                    n
                                  /===\
                                   ! !    1
(%o10)                             ! !  -----
                                   ! !  k + 1
                                  k = 1
(%i11) product (if k <= 5 then a^k else b^k, k, 1, 10);
                                     15  40
(%o11)                              a   b

simpsum
Default value: false.

When simpsum is true, the result of a sum is simplified. This simplification may sometimes be able to produce a closed form. If simpsum is false or if the quoted form 'sum is used, the value is a sum noun form which is a representation of the sigma notation used in mathematics.

sum (expr, i, i_0, i_1)
Represents a summation of the values of expr as the index i varies from i_0 to i_1.

The noun form ‘sum is displayed as an uppercase letter sigma.

sum evaluates its summand expr and lower and upper limits i_0 and i_1, sum quotes (does not evaluate) the index i.

If the upper and lower limits differ by an integer, the summand expr is evaluated for each value of the summation index i, and the result is an explicit sum.

Otherwise, the range of the index is indefinite. Some rules are applied to simplify the summation. When the global variable simpsum is true, additional rules are applied.

In some cases, simplification yields a result which is not a summation; otherwise, the result is a noun form 'sum.

When the evflag (evaluation flag) cauchysum is true, a product of summations is expressed as a Cauchy product, in which the index of the inner summation is a function of the index of the outer one, rather than varying independently.

The global variable genindex is the alphabetic prefix used to generate the next index of summation, when an automatically generated index is needed.

gensumnum is the numeric suffix used to generate the next index of summation, when an automatically generated index is needed. When gensumnum is false, an automatically-generated index is only genindex with no numeric suffix.

See also lsum, sumcontract, intosum, bashindices, niceindices, nouns, evflag, and zeilberger-pkg.

(%i12) sum (i^2, i, 1, 7);
(%o12)                                140
(%i13) sum (a[i], i, 1, 7);
(%o13)                 a  + a  + a  + a  + a  + a  + a
                        7    6    5    4    3    2    1
(%i14) sum (a(i), i, 1, 7);
(%o14)          a(7) + a(6) + a(5) + a(4) + a(3) + a(2) + a(1)
(%i15) sum (a(i), i, 1, n);
                                   n
                                  ====
                                  \
(%o15)                             >    a(i)
                                  /
                                  ====
                                  i = 1
(%i16) sum (2^i + i^2, i, 0, n);
                                 n
                                ====
                                \       i    2
(%o16)                           >    (2  + i )
                                /
                                ====
                                i = 0
(%i17) sum (2^i + i^2, i, 0, n), simpsum;
                                     3      2
                          n + 1   2 n  + 3 n  + n
(%o17)                   2      + --------------- - 1
                                         6
(%i18) sum (1/3^i, i, 1, inf);
                                   inf
                                   ====
                                   \     1
(%o18)                              >    --
                                   /      i
                                   ====  3
                                   i = 1
(%i19) sum (1/3^i, i, 1, inf), simpsum;
                                       1
(%o19)                                 -
                                       2
(%i20) sum (i^2, i, 1, 4) * sum (1/i^2, i, 1, inf);
                                     inf
                                     ====
                                     \     1
(%o20)                            30  >    --
                                     /      2
                                     ====  i
                                     i = 1
(%i21) sum (i^2, i, 1, 4) * sum (1/i^2, i, 1, inf), simpsum;
                                         2
(%o21)                              5 %pi
(%i22) sum (integrate (x^k, x, 0, 1), k, 1, n);
                                   n
                                  ====
                                  \       1
(%o22)                             >    -----
                                  /     k + 1
                                  ====
                                  k = 1
(%i23) sum (if k <= 5 then a^k else b^k, k, 1, 10);
                 10    9    8    7    6    5    4    3    2
(%o23)          b   + b  + b  + b  + b  + a  + a  + a  + a  + a

sumcontract (expr)
Combines all sums of an addition that have upper and lower bounds that differ by constants. The result is an expression containing one summation for each set of such summations added to all appropriate extra terms that had to be extracted to form this sum. sumcontract combines all compatible sums and uses one of the indices from one of the sums if it can, and then try to form a reasonable index if it cannot use any supplied.

It may be necessary to do an intosum (expr) before the sumcontract.

sumexpand
Default value: false.

When sumexpand is true, products of sums and exponentiated sums simplify to nested sums.

See also cauchysum.

(%i24) sumexpand: true$

(%i25) sum (f (i), i, 0, m) * sum (g (j), j, 0, n);
                            m      n
                           ====   ====
                           \      \
(%o25)                      >      >     f(i1) g(i2)
                           /      /
                           ====   ====
                           i1 = 0 i2 = 0
(%i26) sum (f (i), i, 0, m)^2;
                            m      m
                           ====   ====
                           \      \
(%o26)                      >      >     f(i3) f(i4)
                           /      /
                           ====   ====
                           i3 = 0 i4 = 0

Visto nel Web – 374

Oltre la Befana; ecco cosa ho wisto nel Web.

dv1ueu-woaeneu-

A reddit bot that applies machine learning to chess game pictures and extracts the game position! Neat concept. You could extend it to analyse the position too
Python
::: _wilfredh

One crucial factor in Stockfish becoming a leading chess engine is its test framework. Lots of engines have clever programmers, but a strong test technique gave it an extra edge!
applicazioni, programmi
::: _wilfredh

Looking at the increasing dominance of FOSS software in chess programs, I wonder if open source, commoditised implementations are the likely end goal for most software applications. Perhaps professional programming will become largely glue/business logic?
open source
::: _wilfredh

As promised, I’ve just deactivated my Facebook and Facebook Messenger accounts. I had already shut down my Instagram and WhatsApp accounts
io conto di farlo per tutto gennaio
social media
::: waltmossberg

Could You Live Without Your Smartphone?
dispositivi mobili
::: Slashdot

Nancy Grace Roman, chief of astronomy at NASA, is seen here explaining the Advanced Orbiting Solar Observatory to @TheRealBuzz in 1965. Roman died this week at 93
protagonisti
::: LegoNASAWomen

On this day in 1903 was born John von Neumann, the greatest polymath of the 20th century
protagonisti
::: rodneyabrooks

What do self-driving cars, Netflix and space robots have in common? One guess…
Ubuntu
::: omgubuntu

Considered by many to be one of the best combinatorial books; Applied Combinatorics by Alan Tucker
manuali, how to | matematica
::: mathematicsprof

After all these billions of years, version 0 of @jefferickson’s algorithms textbook is complete and available for immediate theft!
manuali, how to | algoritmi, codice
::: GarbledCircus

4 charts on how people around the world see education
scuola, educazione
::: pewresearch

44505636_10217570191394988_3535066115367501824_n

Wrapping up 2018 with a little startup-focused (and somewhat self-centered) preview of what’s coming in OpenJDK 12
linguaggi di programmazione
::: cl4es

Revenue generated each hour
economia, lavoro
::: JonErlichman

The IBM 029 card punch machine explained by @TwoBitHistory
storia
::: adrbaez

The United States has ceded leadership in cyberspace to China
Web, Internet
::: ForeignAffairs

Great context on today’s Corman Lisp 3.1 release
solo Windows, nèh!
lisp(s)
::: xach

Several Popular Apps Share Data With Facebook Without User Consent
Facebook
::: Slashdot ::: DuckDuckGo ::: megangrA ::: marcelsalathe ::: jeanqasaur ::: Slashdot ::: AntonioCasilli ::: opiniojuris ::: waltmossberg ::: FrankPasquale ::: fabiochiusi ::: oliviasolon

Lawrence Roberts, Who Helped Design Internet’s Precursor, Dies at 81
protagonisti
::: Slashdot

Selling electronic goods with instructions used to be the norm. It’s much rarer now
il mio RTFM doce ca a finire? online, ovviamente 😋
manuali, how to
::: _wilfredh

#GooglePlus anticipa la sua chiusura ad aprile 2019. La causa è un bug che potenzialmente interessa 52,5 milioni di utenti. Tuttavia, la principale ragione dello shut down è che il 90% delle sessioni utente ha una durata inferiore ai 5 secondi
social media
::: SergioGridelli

The State of Desktop Linux 2019 | A snapshot of the current state of #Desktop #Linux at the start of 2019—with comparison charts and a roundtable Q&A with the leaders of three top Linux distributions
Linux
::: linuxjournal

Dependent Types at Work
programmazione funzionale
::: FunctorFact

dqdojpjx0aabvyg

China Gets on the Bandwagon To Provide Global Satellite Internet
Web, Internet
::: Slashdot

I wanted to get this out, a set of projects that will help me learn @racketlang , and I hope may be of use to others
per Raspberry Pi
language Racket | hardware
::: zosho

Emacs calculator
tools, componenti software
::: UnixToolTip

WhatsApp update will bring ADS to the popular messaging platform in the New Year
social media | ad, pubblicità
::: Gianlucadfiore

Klipse now supports Prolog! Now we can learn Prolog without leaving the browser. Yeah🤓
programming, codice, snippet | Web, Internet
::: viebel

Memory-level parallelism: Intel Skylake versus Intel Cannonlake
hardware
::: lemire

97% of teen boys in the U.S. play video games on some kind of device
games
::: pewresearch

Let 2019 be the year when flat UI design dies and we go back to subtle skeuomorphism and bordered buttons
programming, codice, snippet
::: glebd

On August 3, 2018, Facebook went offline for about 45 minutes. Seconds after the platform malfunctioned, users clicked over to news outlets. In an analysis of more than 4,000 publishers’ sites, direct traffic increased 11 percent during Facebook’s lapse
Web, Internet | social media
::: WIRED

Learn eBPF Tracing — beginner, intermediate, and advanced
programming, codice, snippet
::: brendangregg

6 years of Raspberry Pi
sistemi operativi | hardware
::: dcavedon

drjxn80x4aalvjd

Five weeks after the Guardian’s viral blockbuster Assange/Manafort scoop, no evidence has emerged – just stonewalling
Web, Internet
::: fabiochiusi

News media of the future could be as messy, diverse, and riotously disputatious as their audiences, because directly monetizing them is the new central challenge of the news business
media | economia, lavoro
::: fabiochiusi

GIMP Developers Outline Plan For 2019
applicazioni, programmi
::: Slashdot

Larry Roberts, who died on Dec. 26, was key to developing the Internet as we know it based on packet switching. But he made the case back in 2009 for a radical new routing technique called flow management
protagonisti
::: IEEESpectrum

Compiling with Continuations, or without? Whatever
programming, codice, snippet
::: wilbowma

Fortnite Star Ninja Says He Raked in Millions of Dollars Last Year
games
::: Slashdot

It’s 2019 and Python 2 is slowly trickling out of the PyData stack
Python
::: jakevdp

Who I Want to Hire
economia, lavoro | programming, codice, snippet
::: RichRogersIoT

Letter from Tim Cook to Apple investors. Let’s brace for an economically challenging 2019
ditte | economia, lavoro
::: marcelsalathe ::: stratechery ::: business
Scratch 3.0 is here!
linguaggi di programmazione | scuola, educazione
::: scratch ::: seanhic ::: LindaIerardi ::: ScratchEdTeam ::: TechIgnites ::: mres ::: jacopo_iacoboni ::: Slashdot ::: emenietti ::: quinta ::: fabiochiusi

Hackers Are Taking Over Chromecasts To Promote a YouTube Channel
social media
::: Slashdot

dvmainpu0aamqtb

Ajit Pai Thanks Congress For Helping Him Kill Net Neutrality Rules
Web, Internet
::: Slashdot

Thanks to the current bizarro world antitrust, Amazon’s quasi-state is allowed to grow larger and ever-more powerful
ditte
::: sandeepvaheesan

Yes, the tech giants are violating the antitrust laws
ditte
::: Sally_Hubbard

Today we release Linspire 8.0
Linux distro
::: LinspireLinux

Migrating from Google Analytics
Web, Internet
::: Gianlucadfiore

Platform distribution, one form of: “The reality is that the most valuable real estate in the world is the top fold of Netflix home page. And Netflix not only controls it, they don’t rent it to anyone”
media
::: rasmus_kleis

Video Games Now Account For More Than Half of UK Entertainment Market
games
::: Slashdot

Google Shifted $23 Billion To Tax Haven Bermuda in 2017, Filing Shows
ditte | frodi
::: Slashdot

I will again recommend everyone spend some time working through some of the book. It’s may be a bit daunting and a barrier to have to get Lisp/Emacs and Slime setup, but it’s worth the experience of working through the exercises in the book
sì, uno dei migliori che ho studiato; diponibile online
lisp(s)
::: dan_ballard

A new version of ExTiX Linux Live DVD—19.1, build 181228—was released yesterday. The author says it’s “So easy that a ten year child can do it!”
Linux distro
::: linuxjournal

dveaturu0aa9afp

Software that has a @SwHeritage Release id, as described in @wikidata
open source | Web, Internet
::: WikiDigi

Programming languages differ massively in the range of numeric types they offer
linguaggi di programmazione
::: _wilfredh

We are happy to announce that we are open sourcing our support for using #Docker Compose on @kubernetesio
open source
::: Docker

Google’s Fuchsia OS Confirmed To Have Android App Support Via Android Runtime
sistemi operativi | dispositivi mobili
::: Slashdot

TIL Google Domains offers free Dynamic DNS. Won’t be paying DynDNS in the future
Web, Internet
::: wesmckinn

CoderDojo – a free programming club for kids by Mishari Muqbil – Talk covers the overall structure & concepts of CoderDojo, why you should set one up, lessons learned after operating CoderDojo for a year & why community-driven education is the future
scuola, educazione
::: ThePSF

Learning a new skill by putting in 45 minutes a day for a month
scuola, educazione
::: Gianlucadfiore

Coding on an iPad Pro in 2019
programming, codice, snippet
::: Gianlucadfiore

TIL Mosaic was not the first web browser, but it played a pivotal role in popularising the world wide web and making it accessible to normal computer users
storia | Web, Internet
::: _wilfredh

$ sudo apt install beancount fava i.e., both #Beancount and #Fava are now available in #Debian unstable; they should hit testing in a couple of days #plaintextaccounting
applicazioni, programmi
::: zacchiro

People are always asking me about when I work and how much I work but it’s not clear that anybody is on the same page about what “work” actually means. To address this I wrote a blog post showing how I’ve spent my working hours from undergrad until now
economia, lavoro
::: jeanqasaur

dwbtolyx4audy8o

Tilix 1.8.7 Released, Here’s How to Install it on Ubuntu
tools, componenti software
::: dcavedon

“Fuzzing Like It’s 1989” super article by @trailofbits where fuzzing tools from 1989 show bugs in today apps…
matti! cioè no, anch’io quando ero giovane; e poi continua a venirmi di usare more invece di less e il Fortran e … OK, posso smettere anzi già fatto
programming, codice, snippet
::: fanf42

Hyundai Joins the Linux Foundation To Embrace AGL’s Open Source Connected Car Tech
Linux
::: Slashdot

See which platforms different age groups turn to for their news in eight Western European countries
media
::: pewjournalism

How YouTube’s Domination of Streaming Clips the Market’s Wings
Web, Internet
::: Slashdot

Allowing users to redefine anything at any point has far reaching design consequences, and has helped lisp/Smalltalk IDEs
“most programmers will probably never have the opportunity to find out whether they prefer it” 😐
programming, codice, snippet
::: _wilfredh

On building business models on top of open source projects
open source
::: _wilfredh

Not everyone in advanced economies is using social media
social media
::: pewinternet

Social media sites have surpassed print newspapers as a news source for Americans: One-in-five U.S. adults say they often get news via social media, slightly higher than the share who often do so from print newspapers
media | social media
::: FactTank

We have recently received confirmation that @wikileaks founder #JulianAssange has been charged in secret so as to have him extradited to the #USA as soon as he can be arrested
Web, Internet
::: DiEM_25

“How is such an absurd structure able to sustain itself—and how might we change it?” @Joi’s latest @WIRED Ideas story tackles academic profit margins, impact factors, and the Open Access movement
open source
::: medialab

dwf5nubw0aixwco

Ethereum Plans To Cut Its Absurd Energy Consumption By 99 Percent
blockchain e crypto*
::: Slashdot

Netflix’s New iTunes Billing Policy Will Curb a $256 Million Revenue Stream For Apple
economia, lavoro
::: Slashdot

Will the World Embrace Plan S, the Radical Proposal To Mandate Open Access To Science Papers?
open source
::: Slashdot

With the exception of YouTube, no other major social media platform comes close to Facebook in terms of usage
social media
::: pewresearch ::: pewresearch

Salvini dimezzato sui social. Grillo che precipita di 30mila posizioni. Rousseau che perde il 30% di iscritti e ora ha molto meno seguito del solo @insopportabile (absit iniuria verbis, my friend… 😎). Sarà anche populismo, ma in rete è sempre meno popolare. Zeitgeist…
social media
::: carloalberto

An Introduction to Julia (Beginner Level) by Jane Herriman Sacha Verweij – Talk provides an overview of Julia’s syntax, core language features such as multiple dispatch, standard library functionality, & package system
linguaggi di programmazione
::: ThePSF

#UE finanzia il #SoftwareLibero cui fa già affidamento, da buona cittadina delle rispettive comunità
open source
::: WikimediaItalia ::: linuxjournal

Even a mind as great as Huygens did not understand second derivatives. He asked Leibniz why they were worth learning
ah! la mate 💡 e senza Maxima, Octave e Matplotlib 💡
storia
::: stevenstrogatz

The share of Americans who go online, use social media or own key devices has remained stable the past two years
Web, Internet | social media
::: pewresearch

21 years ago this week, Apple (then Apple Computer) was officially incorporated. From the archives, here’s our story about the Vintage Computer Festival East, which features Apple’s first product, the now very rare Apple I
storia
::: IEEESpectrum

pig