FEniCS / ufl / 34579120279

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Give each pull back an inverse (#511)

* Fix Interpolate holes

* Interpolate._cache

* Expose Interpolate to the form compiler

* Fix shape and negation

* ruff

* Fix mypy

* Give a base form operator all of its domains

A base form operator's argument slots are not among its operands, so
traversing the operands misses the domains they are defined over. An
interpolation onto a point cloud is the case that notices: the target is
reachable only through the dual argument, and the form compiler numbers
its domains against this list.

extract_unique_domain still answers with the operand's domain, which is
where the operator takes its value.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

* ruff

* Give every base form operator its domain analysis

BaseForm requires _analyze_domains and ufl_domains of its subclasses, and
BaseFormOperator never supplied them: Interpolate carried the pair alone, so
every other operator fell through to the deprecated Expr.ufl_domains, which
answers by calling extract_domains and recurses forever now that
extract_domains routes a base form operator back through it. Differentiating
an interpolation is the case that notices, as BaseFormOperatorDerivative has
no such override.

The analysis reads ufl_operands and argument_slots, both of which every base
form operator has, so it belongs on the base class unchanged.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

* Negate a base form operator through its parent type

Interpolate.__neg__ chose between the expression and the form negation by
testing is_dual(self._function_space), the interpolation's target space. That
space stays primal even when the interpolation is itself a form, so negating an
Interpolate built against a Cofunction gave a Product while multiplying the
same object by -1 gave a FormSum.

None of the other arithmetic operators consult the target space. __add__,
__radd__, __mul__ and __rmul__ all dispatch through _parent_type, which tests
is_dual(self... (continued)

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