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Re: Up-Values with GroebnerBasis
*To*: mathgroup at smc.vnet.net
*Subject*: [mg19436] Re: [mg19424] Up-Values with GroebnerBasis
*From*: "Clifford J. Nelson" <cnelson9 at gte.net>
*Date*: Wed, 25 Aug 1999 01:25:10 -0400
*References*: <7ptaqh$lj4@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
"Ersek, Ted R" wrote:
> Cliff Nelson wrote:
> ------------------------
> The Solve function in Mathematica version 3.0.1 uses GroebnerBasis but
> GroebnerBasis does not use up-values with which I define my own kind of
> numbers. So, how can I use Solve to quickly find solutions to equations
> with coefficients which have up-values for addition, subtraction,
> multiplication, division, and powers defined by my own rules for B
> numbers(a list of numbers wrapped by the head B[{a,b,...}]) in version
> 3.0.1? It works fine in version 2.1, 2.2 and 2.2.2.
>
> ------------------------
>
> Are you sure the kernel isn't ignoring your up-values for addition,
> subtraction, and
> multiplication? In Mathematica Version 3 and 4 the kernel uses built-in
> rules for Plus, Times before user defined rules (including your upvalues).
> I recommend you start by looking into that.
>
> As to how you can use Solve to quickly find solutions:
> - I don't really understand your problem.
> - I only have a vague understanding of GroebnerBasis.
>
> But if you send in an example you will probably get a solution. Keep in
> mind the probability of a good solution is inversely proportional to the
> length of your example.
>
> -------------------------
> Regards,
> Ted Ersek
>
> For Mathematica tips, tricks see
> http://www.dot.net.au/~elisha/ersek/Tricks.html
( http://forum.swarthmore.edu/epigone/geometry-research/brydilyum ) is where
you can find the links to mathsource for the package with the up-values from
RBFields.m. This is long. I hope someone can get it to work. Maybe Method ->
n in the Solve function or something like that? The answers to the two Solve
statements should be the same. Thank you for your time.
Cliff Nelson
In[1]:=
<<RBFields.m
Out[1]=
{"E"}
In[2]:=
GroebnerBasis[{x 2,x y 3}]
Out[2]=
{x}
In[3]:=
GroebnerBasis[{x B[{2,2,-4}],x y B[{3,3,-6}]}]
Out[3]=
{x*y*B[{3, 3, -6}], x*B[{2, 2, -4}]}
In[4]:=
m= {{x,y},{xx,yy}}
Out[4]=
{{x, y}, {xx, yy}}
In[5]:=
divv[x_] := (Plus @@({v,1} First[x]))/(Plus @@ ( {v,1} Last[x]))
In[6]:=
eq = Range[5]
Out[6]=
{1, 2, 3, 4, 5}
In[7]:=
exeq = ( divv/@ NestList [m.#&,m,4]) - eq;
In[8]:=
Solve[exeq=={0,0,0,0,0},{v,x,xx,y,yy}]
>From In[8]:=
Solve::svars: Equations may not give solutions for all "solve" variables.
Out[8]=
{{v -> 0, y -> yy, x -> yy, xx -> 0}}
In[9]:=
beq = N[ {B[{1,1,-2}],B[{2,2,-4}],B[{3,3,-6}],B[{4,4,-8}],B[{5,5,-10}]}]
Out[9]=
{B[{1., 1., -2.}], B[{2., 2., -4.}], B[{3., 3., -6.}], B[{4., 4., -8.}],
B[{5., 5., -10.}]}
In[10]:=
exbnumeq = ( divv /@ NestList [m.#&,m,4]) - beq;
In[11]:=
Solve[exbnumeq=={0,0,0,0,0},{v,x,xx,y,yy}]
Out[11]=
$Aborted
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