symbolic-computation

问题 I define two matrices mat1 and mat2 in Sym class which is suitable for Ryacas symbolic computation: library(Ryacas) x <- Sym("x") mat1 <- List( List(x, 2), List(x^3, x)) and mat2 <- List( List(x, x), List(3, 6 * x)) now the question is how I can have the symbolic multiplication of these two matrices by Ryacas package? Thank you in advance. 回答1: Try this: > mat1 * mat2 expression(list(list(x^2 + 6, x^2 + 12 * x), list(x^4 + 3 * x, x^4 + 6 * x^2))) 来源： https://stackoverflow.com/questions

问题 I'm working on transformation polynomial systems over GF(2^N) to GF(2). In a process of transformation I need to do lots of modulo 2 computations like summing and multiplying matrices. So is there way to sum and multiply matrices using modulo 2 arithmetics in Sympy? 回答1: I've had luck with sympy's trunc() function: from sympy import * var('x:z') y=25*x+12 z=trunc(y,2) # z=x 来源： https://stackoverflow.com/questions/21660852/modulo-2-arithmetics-in-sympy

问题 Please consider this example. I would like to solve x^3 - 2x > 0. I try the following commands: syms x; f = @(x) x^3-2*x; solve(f(x)>0,x) and Matlab returns this ans = solve([0.0 < x^3 - 2.0*x], [x]) which is not what I expect. Therefore I use solve(f(x)+x>x,x) which returns ans = Dom::Interval(2^(1/2), Inf) Dom::Interval(-2^(1/2), 0) Can someone explain that why solve works successfully only in the second case? 回答1: Try adding the Real option to solve : solve(f(x)>0,x,'Real',1) ans = Dom:

问题 I have Symbolic C++ (the version that can integrate with V, there is no documentation on how to install it. I got it from this website and it has examples of how it work: http://issc.uj.ac.za/symbolic/symbolic.html Does anyone have any idea on how to install this to use with my projects in Visual Studio? 回答1: Maybe a late answer, but may still be useful for others. For *nix systems: There are two versions: [1] Tarball that do not need to be installed in your system: http://issc.uj.ac.za

问题 I have the following expression: from sympy import pi, sin, cos, var, simplify var('j,u,v,w,vt,wt,a2,t,phi') u0 = v*a2*sin(pi*j/2 + pi*j*t*phi**(-1)/2) + pi*vt*a2*cos(pi*j/2 + pi*j*t*phi**(-1)/2)*j*phi**(-1)/2 + pi*w*a2*cos(pi*j/2 + pi*j*t*phi**(-1)/2)*j*phi**(-1) Which can be simplified: print simplify(u0) #a2*(pi*j*vt*cos(pi*j*(phi + t)/(2*phi)) + 2*pi*j*w*cos(pi*j*(phi + t)/(2*phi)) + 2*phi*v*sin(pi*j*(phi + t)/(2*phi)))/(2*phi) Given the sub-expressions: bj = pi*j*(phi + t)/(2*phi) cj = j

问题 MATLAB sinc(0) will return 1 as it should. But sinc(K) of some symbol K for which a value of zero is substituted will return NaN. The following code illustrates the above: sinc(0) % calculate sinc of 0, this will return 1 K = sym('K'); % define symbol K % try to substitute value 0 for K in sinc(K), this will return NaN subs(sinc(K), K, 0) Can I force sinc to return 1 in the symbolic case (without knowing the value of K in advance)? MATLAB Version: 8.0.0.783 (R2012b) Symbolic Math Toolbox

问题 I need to do analytical integration in C++. For example, I should integrate expressions like this: exp[I(x-y)] , I is an imaginary number. How can I do this in C++? I tried GiNaC but it can just integrate polynomials. I also tried SymbolicC++. It can integrate functions like sine , cosine or exp(x) and ln(x) , but it is not very powerful. For example, it can not integrate x*ln(x) which can be easily obtained by use of Mathematica or by integration by parts. Are there any other tools or

问题 The following command syms x real; f = @(x) log(x^2)*exp(-1/(x^2)); fp(x) = diff(f(x),x); fpp(x) = diff(fp(x),x); and solve(fpp(x)>0,x,'Real',true) return the result solve([0.0 < (8.0*exp(-1.0/x^2))/x^4 - (2.0*exp(-1.0/x^2))/x^2 - (6.0*log(x^2)*exp(-1.0/x^2))/x^4 + (4.0*log(x^2)*exp(-1.0/x^2))/x^6], [x == RD_NINF..RD_INF]) which is not what I expect. The first question: Is it possible to force Matlab's solve to return the set of all solutions? (This is related to this question.) Moreover,

问题 The DO dialect uses series of category PAREN! for precedence, and will usually boil away the underlying parentheses structure prior to invoking a function. However, it used to be possible in Rebol 2 to specify in a function's definition that you wanted it to suppress evaluation of parentheses at the callsite. You did this by using a "literal word" apostrophe mark on a parameter: evaluated: func [param] [probe param] non-evaluated: func ['param] [probe param] >> evaluated (1 + 2) 3 >> non

问题 In sympy I have an integral which returns a Piecewise object, e.g. In [2]: from sympy.abc import x,y,z In [3]: test = exp(-x**2/z**2) In [4]: itest = integrate(test,(x,0,oo)) In [5]: itest Out[5]: ⎧ ___ ⎪ ╲╱ π ⋅z │ ⎛ 1 ⎞│ π ⎪ ─────── for │periodic_argument⎜──────────────, ∞⎟│ ≤ ─ ⎪ 2 │ ⎜ 2 ⎟│ 2 ⎪ │ ⎝polar_lift (z) ⎠│ ⎪ ⎪∞ ⎪⌠ ⎨⎮ 2 ⎪⎮ -x ⎪⎮ ─── ⎪⎮ 2 ⎪⎮ z ⎪⎮ ℯ dx otherwise ⎪⌡ ⎪0 ⎩ I would like to extract just the first branch of this piecewise equation, in other words, I would like to be able to