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### "det" in pdl and "det" in polymake

Posted: 09 Aug 2020, 04:17
Hi,

I have written a script that uses pdl to do some linear algebra computations. In the same script, I'm trying to do a linear algebra computation using the matrix class in polymake.

The issue I'm encountering is that when I apply det to a polymake matrix, it does the pdl det and gives an error. I want to use the polymake det function because I'm running into numerical precision issues with the pdl det (if I replace all the matrices by pdl matrices).

Is there a way to tell polymake to use the polymake det function? If not, is there is an efficient way to compute the multiplicity of a set of integer vectors (i.e., the index of the subgroup of lattice points they generate in the group of lattice points in the vector space they span) in polymake?

Thank you!

### Re: "det" in pdl and "det" in polymake

Posted: 11 Aug 2020, 16:51
Is there a way to tell polymake to use the polymake det function?
This is impossible to answer without seeing your script. I do not know about pdl. That is, if you would post that script, it might require a bit of explanation.
If not, is there is an efficient way to compute the multiplicity of a set of integer vectors (i.e., the index of the subgroup of lattice points they generate in the group of lattice points in the vector space they span) in polymake?
Well, that's clearly a determinant computation.

### Re: "det" in pdl and "det" in polymake

Posted: 12 Aug 2020, 02:08
I guess my question is: Is there a way to give the "det" function in polymake an alias so that I can call it, even though "det" in pdl has the same name?

That said, here is (the relevant pieces) of my code.
First I have a function that computes multiplicity using polymake's "det" function

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```sub multiplicityArray{ my @input = @{shift @_}; my @vecs = map(latticePointToArray(\$_), @input); my \$num = scalar(@vecs); my @minors = subsets([0..scalar(@{\$vecs})-1], \$num); my @minorsDets; for my \$sub(@minors){ my @matrixAoa = (); for my \$i(0..(\$num - 1)){ my @row = (); for my \$j (0..(\$num - 1)){ push(@row, \$vecs[\$i]->[\$sub->[\$j]]); } push(@matrixAoa, \@row); } my \$a = new Matrix<Int>(\@matrixAoa); my \$d = det(\$a); push(@minorsDets, \$d); } my \$v = new Vector<Int>(\@minorsDets); return \$gcd(\$v); } ```
In various other places, I use pdl to do things like compute the inverse of a matrix. For example, I have the following function.

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```use PDL; sub returnLinearExpression{ my \$diagram = shift; my \$facet = shift; my \$dim = scalar(@{\$facet}) - 1; my @coords = (); for my \$i (0..\$dim){ push(@coords, \$diagram->[\$facet->[\$i]]); } my @row = (1) x (\$dim + 1); my \$r = pdl[\@row]; my \$target = \$r->transpose; #now creates the matrix of the coords my \$tpose = pdl[\@coords]; my \$mat = \$tpose->transpose; my \$inv = inv(\$mat); my \$res = \$inv x \$target; my @res = \$res->list; return \@res; } ```

### Re: "det" in pdl and "det" in polymake

Posted: 12 Aug 2020, 02:27
Of course I could write my own function to compute the determinant of a polymake matrix, I was just wondering if there is an easy way around this.

### Re: "det" in pdl and "det" in polymake

Posted: 12 Aug 2020, 03:22
Now I see that the function "pluecker" does exactly what I want. So that provides a (better) work around.

Thank you!

### Re: "det" in pdl and "det" in polymake

Posted: 12 Aug 2020, 09:22
I am glad you found something useful in polymake.

Let me point out that polymake scripts differ slightly from general perl scripts. They should start out with something like

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```use application "polytope"; ```
to set the scope (i.e., the active application). polymake's determinant function lives in the application common. So you can force calling this function by

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```my \$d = common::det(\$a); ```