Is Axiom Good For Knot Theory?

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Hi All,
I=E2=80=99ve recently discovered Axiom and was wondering if it would be app=
ropriate
for computing the kei quandle in Knot Theory. It essentially amounts to
looking up values in a multiplication table - only the operation is non
commutative.

I wind up with these nested expressions and am trying to write a program to
quickly solve them - ex. 9 =E2=96=B7 (6 =E2=96=B7 0)

I tried Sage math, but it didn't really do what I wanted as far as i could
tell. I've been working on a tool to do this in Python, but it's kind of
hard to do analytical stuff like telling when two different expressions
might be equal or reduced or not. Ex. Knowing when 9 =E2=96=B7 (6 =E2=96=B7=
 0) =3D=3D (9 =E2=96=B7 6) =E2=96=B7
 (9 =E2=96=B7 0)

In short, can Axiom or other CAS systems handle non-standard binary
operations and reduce expressions? Would you be able to direct me to such a
tool?

Thanks for all the help! I hope I'm using the correct mailing list.
Anthony

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<div dir=3D"ltr">Hi All,<div dir=3D"auto">I=E2=80=99ve recently discovered =
Axiom and was wondering if it would be appropriate for computing the kei qu=
andle in Knot Theory. It essentially amounts to looking up values in a mult=
iplication table - only the operation is non commutative.=C2=A0</div><div d=
ir=3D"auto"><br></div><div dir=3D"auto">I wind up with these nested express=
ions and am trying to write a program to quickly solve them - ex.<font colo=
r=3D"#000000">=C2=A0<span style=3D"font-family:&quot;Helvetica Neue&quot;;f=
ont-size:10px">9 </span><span class=3D"gmail-s1" style=3D"font-variant-nume=
ric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;fo=
nt-kerning:auto;font-feature-settings:normal;font-stretch:normal;font-size:=
10px;line-height:normal;font-family:&quot;Hiragino Sans&quot;">=E2=96=B7</s=
pan><span style=3D"font-family:&quot;Helvetica Neue&quot;;font-size:10px"> =
(6 </span><span class=3D"gmail-s1" style=3D"font-variant-numeric:normal;fon=
t-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:aut=
o;font-feature-settings:normal;font-stretch:normal;font-size:10px;line-heig=
ht:normal;font-family:&quot;Hiragino Sans&quot;">=E2=96=B7</span><span styl=
e=3D"font-family:&quot;Helvetica Neue&quot;;font-size:10px"> 0)=C2=A0</span=
></font></div><div dir=3D"auto"><br></div><div>I tried Sage math, but it di=
dn&#39;t really do what I wanted as far as i could tell. I&#39;ve been work=
ing on a tool to do this in Python, but it&#39;s kind of hard to do analyti=
cal stuff like telling when two different expressions might be equal or red=
uced or not. Ex. Knowing when=C2=A0<span style=3D"color:rgb(0,0,0);font-fam=
ily:&quot;Helvetica Neue&quot;;font-size:10px">9=C2=A0</span><span class=3D=
"gmail-s1" style=3D"font-variant-numeric:normal;font-variant-east-asian:nor=
mal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:=
normal;font-stretch:normal;font-size:10px;line-height:normal;font-family:&q=
uot;Hiragino Sans&quot;;color:rgb(0,0,0)">=E2=96=B7</span><span style=3D"co=
lor:rgb(0,0,0);font-family:&quot;Helvetica Neue&quot;;font-size:10px">=C2=
=A0(6=C2=A0</span><span class=3D"gmail-s1" style=3D"font-variant-numeric:no=
rmal;font-variant-east-asian:normal;font-variant-alternates:normal;font-ker=
ning:auto;font-feature-settings:normal;font-stretch:normal;font-size:10px;l=
ine-height:normal;font-family:&quot;Hiragino Sans&quot;;color:rgb(0,0,0)">=
=E2=96=B7</span><span style=3D"color:rgb(0,0,0);font-family:&quot;Helvetica=
 Neue&quot;;font-size:10px">=C2=A00) =3D=3D (</span><span style=3D"color:rg=
b(0,0,0);font-family:&quot;Helvetica Neue&quot;;font-size:10px">9=C2=A0</sp=
an><span class=3D"gmail-s1" style=3D"font-variant-numeric:normal;font-varia=
nt-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-=
feature-settings:normal;font-stretch:normal;font-size:10px;line-height:norm=
al;font-family:&quot;Hiragino Sans&quot;;color:rgb(0,0,0)">=E2=96=B7</span>=
<span style=3D"color:rgb(0,0,0);font-family:&quot;Helvetica Neue&quot;;font=
-size:10px">=C2=A06)=C2=A0</span><span class=3D"gmail-s1" style=3D"font-var=
iant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:=
normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;f=
ont-size:10px;line-height:normal;font-family:&quot;Hiragino Sans&quot;;colo=
r:rgb(0,0,0)">=E2=96=B7</span><span style=3D"color:rgb(0,0,0);font-family:&=
quot;Helvetica Neue&quot;;font-size:10px">=C2=A0(</span><span style=3D"colo=
r:rgb(0,0,0);font-family:&quot;Helvetica Neue&quot;;font-size:10px">9=C2=A0=
</span><span class=3D"gmail-s1" style=3D"font-variant-numeric:normal;font-v=
ariant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;f=
ont-feature-settings:normal;font-stretch:normal;font-size:10px;line-height:=
normal;font-family:&quot;Hiragino Sans&quot;;color:rgb(0,0,0)">=E2=96=B7</s=
pan><span style=3D"color:rgb(0,0,0);font-family:&quot;Helvetica Neue&quot;;=
font-size:10px">=C2=A00</span><span style=3D"color:rgb(0,0,0);font-family:&=
quot;Helvetica Neue&quot;;font-size:10px">)</span></div><div><br></div><div=
>In short, can Axiom or other CAS systems handle non-standard binary operat=
ions and reduce expressions? Would you be able to direct me to such a tool?=
</div><div><br></div><div>Thanks for all the help! I hope I&#39;m using the=
 correct mailing list.</div><div>Anthony=C2=A0</div>
























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