After some sleep I decided to go for the simple thing first. In
particular, I want to restrict myself to fricas. Here is a list of things
todo on the sage side:
1) implement a method that (reliably!) yields a tuple (type, 1d algebra
output, 2d algebra output, error message, etc) as strings. 1d algebra
output should come in "unparsed inputform" as one very long string, I'd
say. 2d algebra output should be empty if 1d output is available.
It should be able to deal with very long lines, too, possibly be using file
io. This involves use of ioHook and some regexps.
2) implement a method that translates fricas output into sage types.
I think this could work as follows: we want to map fricas types to sage
constructors, possibly recursively. Recall that what's really sent to
fricas is something like "sage23 := [x^n/y^n for n in 1..3]", so that sage
can access the result using the variable "sage23". This string is referred
to as self._name
Now what I propose is a method which takes a parsed type, e.g., "Integer"
or ("List", "Integer") or
("UnivariatePolynomial", "x", ("Fraction", "Integer"))
def to_sage(type):
if type == "Integer":
return to_sage_integer()
elif type == "String":
return to_sage_string()
...
elif isinstance(type, tuple):
if type[0] == "List":
return to_sage_list(type[1])
elif type[0] == "Fraction":
return to_sage_fraction(type[1])
....
and so on.
So, if the type is ("List" ("Fraction" ("UnivariatePolynomial" "x"
"Integer"))), this method would call
to_sage_list(("Fraction" ("UnivariatePolynomial" "x" "Integer"))
which might be something like
def to_sage_list(self, type):
n = fricas.eval("#" + self._name).to_sage_integer()
return [fricas.eval(self._name + ".%n").to_sage(type) for n in
range(1,n+1)]
I'm not sure whether this is clever. What do you think?
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