Fwd: One missing maxima feature, that I have the math behind, but not a program
Subject: Fwd: One missing maxima feature, that I have the math behind, but not a program
From: Mike Valenzuela
Date: Sat, 21 Dec 2013 16:25:47 -0700
The second parameter is your parameter of time, it should be a variable
like t, which you can then plug in a value for. I'm working on something
that does matrices with zero eigenvalues correctly.
On Sat, Dec 21, 2013 at 6:21 AM, Barton Willis <willisb at unk.edu> wrote:
> Examples:
>
>
> (%i2) m : matrix([5,7],[9,11])$
>
>
> Suboptimal?
>
>
> (%i3) matrix_power(m,0);
> expt: undefined: 0^0
>
> 0: matrix_power(a=matrix([5,7],[9,11]),t=0)(mp.mac line 35)
>
>
> For the 0-th power, matrixfun gives the identity:
>
>
> (%i4) matrixfun(lambda([x], x^0), m);
> (%o4) matrix([1,0],[0,1])
>
>
> For an inverse, matrix_power returns a scalar
>
>
> (%i5) matrix_power(m,-1);
> (%o5) B_[2]/(3*2^(3/2)+8)+B_[1]/(8-3*2^(3/2))
>
>
> (%i6) matrixfun(lambda([x], x^-1), m);
> (%o6) matrix([-11/8,7/8],[9/8,-5/8])
>
>
> (%i9) m : matrix([a,b],[b,c]);
> (%o9) matrix([a,b],[b,c])
>
>
> Symbolic matrices:
>
>
> (%i18) m : matrix([a,b],[b,c]);
> (%o18) matrix([a,b],[b,c])
>
>
> (%i19) matrix_power(m,2);
> (%o19)
> (B_[2]*(sqrt(c^2-2*a*c+4*b^2+a^2)+c+a)^2)/4+(B_[1]*(sqrt(c^2-2*a*c+4*b^2+a^2)-c-a)^2)/4
>
>
>
> (%i20) matrixfun(lambda([x],x^2),m);
> Proviso: assuming c^2-2*a*c+4*b^2+a^2 # 0
> (%o20) matrix([b^2+a^2,b*c+a*b],[b*c+a*b,c^2+b^2])
>
>
> --Barton (author of matrixfun)
>
>
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>