non-commuting issue with partitions_()

[crmafra]

The following code is partitioning the arguments without respecting the ordering of the functions:

    ```
    Function I,tmpF1,tmpF2;
    Indices i1,i2;
    Symbol [p];

    L I21 = I(2,1,[p],2,3,4);
    L I12 = I(1,2,[p],2,3,4);

    id I(i1?,i2?,[p],?m) = partitions_(2,tmpF1,i1,tmpF2,i2,?m);
    print +s -f;
   .end

The output with current FORM is:

I21 =

• tmpF1(2,3)*tmpF2(4)
• tmpF1(2,4)*tmpF2(3)

• tmpF1(3,4)*tmpF2(2) ;

  I12 =

• tmpF2(2,3)*tmpF1(4)
• tmpF2(2,4)*tmpF1(3)

• tmpF2(3,4)*tmpF1(2) ;

  The partitioning of function arguments is correct in the second expression but
  the ordering of the functions is not, I would have expected the ordering tmpF1()*tmpF2()
  instead:
  

• tmpF1(4)*tmpF2(2,3)
• tmpF1(3)*tmpF2(2,4)
• tmpF1(2)*tmpF2(3,4)

Is this intentional?

[tueda]

Maybe commutativity was assumed in the code?

[vermaseren]

In the example it looks indeed not so nice, but in general things become too complex if you try to keep track of noncommutability. Imagine partitions_(6,tmpF1,i1,tmpF2,i2,tmpF1,i3,tmpF2,i4,tmpF1,i5,tmpF2,i6,?a) It will be a minor horror now to keep track of the symmetries involved.

In your case, if you want tmpF1 before tmpF2, you use CFunction tmpF1p,tmpF2p; and use those and after that you can use id tmpF1p(?a) = tmpF1(?a); id tmpF2p(?a) = tmpF2(?a); the essence being that you should not do this in a single statement. Now it first gets the tmpF1 and puts them to the left. The second statement now gets the tmpF2 to the right of the tmpF1.

I hope this helps.

Jos

On 28 Oct 2019, at 00:22, Takahiro Ueda notifications@github.com wrote:

Maybe commutativity was assumed in the code?

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[crmafra]

On Mon, 28 Oct 2019 at 1:20:31 -0700, Jos Vermaseren wrote:

In the example it looks indeed not so nice, but in general things become too complex if you try to keep track of noncommutability. Imagine partitions_(6,tmpF1,i1,tmpF2,i2,tmpF1,i3,tmpF2,i4,tmpF1,i5,tmpF2,i6,?a) It will be a minor horror now to keep track of the symmetries involved.

In your case, if you want tmpF1 before tmpF2, you use CFunction tmpF1p,tmpF2p; and use those and after that you can use id tmpF1p(?a) = tmpF1(?a); id tmpF2p(?a) = tmpF2(?a); the essence being that you should not do this in a single statement. Now it first gets the tmpF1 and puts them to the left. The second statement now gets the tmpF2 to the right of the tmpF1.

I hope this helps.

Yes, thank you.

I had a similar workaround here where I would just commute the functions after partitions_().

I decided to raise the issue in case there was an easy fix.

Best regards, Carlos

Jos

On 28 Oct 2019, at 00:22, Takahiro Ueda notifications@github.com wrote:

Maybe commutativity was assumed in the code?

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