Maybe I shoud provide more detailed question. I try to make some
calculus in Sage with noncommutative variables. I know how to do it in
singular, as You may see in example from http://www.sagenb.org/home/pub/1474/
It works ok, but I have problem with switching into sage environment
back. Of course I may copy and paste results, but this is dangerous
because of noncommutativity.
So I try to use examples from
http://groups.google.com/group/sage-support/browse_thread/thread/73ea537d657a3654/ebdc76a97a0b1ea6?lnk=gst&q=noncommutative#ebdc76a97a0b1ea6
And it works. What is not clear to me, is substitutions:
How to use substitution in noncommutative variables when in Sage. I
presume that there is some interface to singular and substitutions
should work, but maybe I am wrong? Is there anybody who can help me,
how to substitute in correct way?
Here is Sage code I try to use:
singular.LIB('ncall.lib')
R=singular.ring(0,'(x,y,z,a,b)','dp')
This are commutativity relations defined by formula: xi*xj=c[i,j]
*xj*xi + d[i,j].
Note that for generators a,b we have pure commutative relations since
C = 1 for this elements
Also below we have definition for D matrix, and for a,b generators
there are D=0 elements, so a,b commute with every other generators.
C=singular.matrix
(5,5,'1,-1,-1,1,1,-1,1,-1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1');C
D=singular.matrix(5,5,'0,0,-y,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0');D
S=C.nc_algebra(D)
S;#Note that below we have noncommutative relations!!!
///
// characteristic : 0
// number of vars : 5
// block 1 : ordering dp
// : names x y z a b
// block 2 : ordering C
// noncommutative relations: ...
S.set_ring()
x=singular('x');x
y=singular('y');y;z=singular('z');z;a=singular('a');a;b=singular
('b');b
x*y
z*x#<- here You see non-zero element from D matrix.
<p><strong>And there are the troubles!!!!</strong></p>
<p><strong>From manual we know that substitute returns the same value
if substitute cannot be performed. So is this this case? Or maybe I
should use direct singular function for substitution? How?</strong></
p>
<p>Examples of substitutions:</p>
f = a*x+ b*y+ 2*z + a*b*x + b*x*a*y;f
f.substitute(x=1);f.substitute(x=y);f.substitute(x=a);
gives:
x*y*a*b+x*a*b+x*a+y*b+2*z
x*y*a*b+x*a*b+x*a+y*b+2*z
x*y*a*b+x*a*b+x*a+y*b+2*z
Which is the same!
Here You may find published worksheet with condes ( and comments) as
above:http://www.sagenb.org/home/pub/1486/
Best Regards!
Kazek Kurz
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