Adding operator Ansätze

sage/period_computation.sage

@@ -1,6 +1,8 @@
 import logging
 from sage.all import sage_eval, PolynomialRing, QQ, SR, log, var
 
+load("sage/util.py")
+
 # Logger
 logger = logging.getLogger(__name__)
 logging.basicConfig(level=logging.DEBUG)
@@ -10,25 +12,66 @@ class PFOperator:
     A class representing a Picard-Fuchs operator in a single variable z.
     Independent of the given order, the variables are assumed to be left of
     the derivatives.
+
+    The variables extra_locals are needed for symbolic coefficients used for
+    operator Ansätze.
     """
-    def _operator_from_string(self, operator_string: str) -> "sage.rings.polynomial.polynomial_ring.Polynomial":
+    def _operator_from_string(self, operator_string: str, extra_locals: dict = None):
         z_names = ['z%d' % i for i in range(self.no_variables)]
         theta_names = ['theta%d' % i for i in range(self.no_variables)]
-        self.ring = PolynomialRing(QQ, z_names + theta_names)
+        base_ring = SR if extra_locals else QQ
+        self.ring = PolynomialRing(base_ring, z_names + theta_names)
         self.z_gens = self.ring.gens()[:self.no_variables]
         self.theta_gens = self.ring.gens()[self.no_variables:]
 
+        parse_locals = dict(self.ring.gens_dict())
+        if extra_locals:
+            parse_locals.update(extra_locals)
+
         try:
-            operator = sage_eval(operator_string, locals=self.ring.gens_dict())
+            operator = sage_eval(operator_string, locals=parse_locals)
+            return operator
         except Exception as e:
             raise ValueError("Invalid operator string: %s" % e)
-        return self.ring(operator)
 
-    def __init__(self, operator_string: str, no_variables: int = 1):
+    def __init__(self, operator_string: str, no_variables: int = 1, extra_locals: dict = None):
         self.no_variables = no_variables
-        self.operator = self._operator_from_string(operator_string)
+        self.operator_string = operator_string
+        self.operator = self._operator_from_string(operator_string, extra_locals=extra_locals)
         logger.info("Initialised PFOperator: %s", self.operator)
 
+class PFOperatorAnsatz(PFOperator):
+    """
+    A class for Picard-Fuchs operator Ansätze, characterised by number of variables and their z- and theta-multi-degrees.
+    """
+    def __init__(self, no_variables: int, theta_degree: int, z_degree: int):
+        self.no_variables = no_variables
+        self.theta_degree = theta_degree
+        self.z_degree = z_degree
+
+        z_indices = _multi_indices(self.no_variables, z_degree)
+        theta_indices = _multi_indices(self.no_variables, theta_degree)
+
+        # Every (z_index, theta_index) pair allowed by the degree bounds gets its own
+        # fresh unknown, to be solved for once the Ansatz is applied to a period.
+        operator_terms = [
+            (var("b_" + "_".join(str(x) for x in z_index + theta_index)), (z_index, theta_index))
+            for z_index in z_indices
+            for theta_index in theta_indices
+        ]
+
+        def _monomial_factors(index, name):
+            return [f"{name}{i}^{exp}" for i, exp in enumerate(index) if exp > 0]
+
+        operator_string = " + ".join(
+            "*".join([str(coeff), *_monomial_factors(z_index, "z"), *_monomial_factors(theta_index, "theta")])
+            for coeff, (z_index, theta_index) in operator_terms
+        )
+
+        extra_locals = {str(coeff): coeff for coeff, _ in operator_terms}
+        super().__init__(operator_string=operator_string, no_variables=no_variables, extra_locals=extra_locals)
+
+
 class Period:
     """
     A class representing a period as a formal power series in z-variables and their logs.
@@ -211,25 +254,13 @@ class PeriodAnsatz(Period):
     A class for period Ansätze, characterised by number of variables and their z- and log-multi-degrees.
     """
 
-    def _multi_indices(self, total_degree: int) -> list:
-        # All no_variables-tuples of non-negative integers whose entries sum to at most total_degree.
-        def helper(remaining_vars, remaining_degree):
-            if remaining_vars == 0:
-                yield ()
-                return
-            for first in range(remaining_degree + 1):
-                for rest in helper(remaining_vars - 1, remaining_degree - first):
-                    yield (first,) + rest
-
-        return list(helper(self.no_variables, total_degree))
-
     def __init__(self, no_variables: int, z_degree: int, log_degree: int):
         self.no_variables = no_variables
         self.z_degree = z_degree
         self.log_degree = log_degree
 
-        log_indices = self._multi_indices(log_degree)
+        log_indices = _multi_indices(self.no_variables, log_degree)
-        z_indices = self._multi_indices(z_degree)
+        z_indices = _multi_indices(self.no_variables, z_degree)
 
         # Every (log_index, z_index) pair allowed by the degree bounds gets its own
         # fresh unknown, to be solved for once a PFOperator is applied to the Ansatz.
@@ -247,3 +278,10 @@ class PeriodAnsatz(Period):
             "Initialised PeriodAnsatz with %d unknown coefficient(s).",
             sum(len(z_dict) for z_dict in self.expansion_coefficients.values()),
         )
+
+
+"""
+To do: 
+    - add method to Period that finds operators that annihilate it (using operator ansatz class)
+    - add class PFideal containing a list of PFOperators
+"""

sage/util.py

@@ -0,0 +1,16 @@
+"""
+Utility functions for the Calabi-Yau period geometry project.
+"""
+
+def _multi_indices(no_variables, total_degree: int) -> list:
+    # All no_variables-tuples of non-negative integers whose entries sum to at most total_degree.
+    def helper(remaining_vars, remaining_degree):
+        if remaining_vars == 0:
+            yield ()
+            return
+        for first in range(remaining_degree + 1):
+            for rest in helper(remaining_vars - 1, remaining_degree - first):
+                yield (first,) + rest
+
+    return list(helper(no_variables, total_degree))
+