Loday-Ronco algebra doesn't allow some CHA methods

[amypang]

I cannot define convolution products in Loday-Ronco. The following shows code that works for QSym but not Loday-Ronco:

LR = algebras.FreeDendriform(QQ)
P = LR.basis()
QSym=QuasiSymmetricFunctions(QQ)
F=QSym.F()

def identitymap():
    def identitymap_(x):
        return x
    return identitymap_

hopfsquareF=F.convolution_product([identitymap(),identitymap()])
hopfsquareP=P.convolution_product([identitymap(),identitymap()])

The last line results in error:

Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1044, in execute
    exec compile(block+'\n', '', 'single', flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
  File "sage/structure/category_object.pyx", line 856, in sage.structure.category_object.CategoryObject.__getattr__ (build/cythonized/sage/structure/category_object.c:8014)
    return self.getattr_from_category(name)
  File "sage/structure/category_object.pyx", line 871, in sage.structure.category_object.CategoryObject.getattr_from_category (build/cythonized/sage/structure/category_object.c:8177)
    attr = getattr_from_other_class(self, cls, name)
  File "sage/cpython/getattr.pyx", line 249, in sage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:1837)
    raise dummy_attribute_error
AttributeError: 'LazyFamily_with_category' object has no attribute 'convolution_product'

This may be related to the fact that the Loday-Ronco basis elements must be specified using square brackets and not round brackets:

sage: F[Compositions(4)[1]]
sage: F(Compositions(4)[1])

F[1, 1, 2]
F[1, 1, 2]

sage: P[BinaryTrees(4)[1]]
sage: P(BinaryTrees(4)[1])

B[[., [., [[., .], .]]]]
Error in lines 2-2
Traceback (most recent call last):
  File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1044, in execute
    exec compile(block+'\n', '', 'single', flags=compile_flags) in namespace, locals
  File "", line 1, in <module>
  File "sage/structure/parent.pyx", line 920, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9377)
    raise NotImplementedError
NotImplementedError

Thanks for your help!

CC: @fchapoton @tscrim @darijgr @saliola @alauve

Component: combinatorics

Keywords: chas

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/25452

[tscrim]

comment:1

That is because P is not what you want. basis returns the basis, not the LR algebra in a particular basis. What you want is

sage: def identity_map(x):
....:     return x
sage: LR.convolution_product([identity_map, identity_map])
Generic endomorphism of Free Dendriform algebra on one generator ['o'] over Rational Field

sage: LR
Free Dendriform algebra on one generator ['o'] over Rational Field
sage: P
Lazy family (Term map from Binary trees to Free Dendriform algebra on one generator ['o'] over Rational Field(i))_{i in Binary trees}

[amypang]

comment:2

Travis, thanks for looking at this. Is there a way to get the LR algebra in the desired basis, so it is in the same style as the other combinatorial Hopf algebras and I can apply convolution_product to it?

[tscrim]

comment:3

LR currently only has 1 basis (implemented), so just use LR like you would, say, F.

[amypang]

comment:4

Thank you Travis! Sorry for making a ticket.

[tscrim]

comment:5

No problem.

[tscrim]

Reviewer: Travis Scrimshaw

[embray]

comment:6

Presuming these are all correctly reviewed as either duplicate, invalid, or wontfix.