README.md

@@ -12,12 +12,21 @@ elliptic_curve_D = ToricPolytopeProjectiveSpace([1, 2, 3], model_name="elliptic_
 
 CY3_quintic = ToricPolytopeProjectiveSpace([1, 1, 1, 1, 1], model_name="quintic")
 CY3_bicubic = ToricPolytopeCICY([[3, 3]], model_name="bi-cubic")
-CICY3_two_parameter_manual_nef = ToricPolytope([[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],
+CICY3_two_parameter_manual_nef = ToricPolytope(
-                                                [0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],
+    [
-                                                [-1,-1,0,0,0,0],[0,0,-1,-1,-1,-1]],
+        [1, 0, 0, 0, 0, 0],
-                                                nef_partition=[[0,1,2,3], [4,5,6,7]])
+        [0, 1, 0, 0, 0, 0],
+        [0, 0, 1, 0, 0, 0],
+        [0, 0, 0, 1, 0, 0],
+        [0, 0, 0, 0, 1, 0],
+        [0, 0, 0, 0, 0, 1],
+        [-1, -1, 0, 0, 0, 0],
+        [0, 0, -1, -1, -1, -1],
+    ],
+    nef_partition=[[0, 1, 2, 3], [4, 5, 6, 7]],
+)
 
-CICY5_two_parameter = ToricPolytopeCICY([[6, 1],[0, 2]])
+CICY5_two_parameter = ToricPolytopeCICY([[6, 1], [0, 2]])
 ```
 
 The discriminant factors and topological data, e.g. for the quintic, can then be computed with the methods below.

sage/period_computation.sage

@@ -1,5 +1,5 @@
 import logging
-from sage.all import sage_eval, PolynomialRing, QQ
+from sage.all import sage_eval, PolynomialRing, QQ, SR, log
 
 class PFOperator:
     """
@@ -7,7 +7,7 @@ class PFOperator:
     Independent of the given order, the variables are assumed to be left of
     the derivatives.
     """
-    def _operator_from_string(self, operator_string):
+    def _operator_from_string(self, operator_string: str) -> "sage.rings.polynomial.polynomial_ring.Polynomial":
         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)
@@ -20,9 +20,182 @@ class PFOperator:
             raise ValueError("Invalid operator string: %s" % e)
         return self.ring(operator)
 
-    def __init__(self, operator_string, no_variables=1):
+    def __init__(self, operator_string: str, no_variables: int = 1):
         self.no_variables = no_variables
         self.operator = self._operator_from_string(operator_string)
-        logging.debug("Initialized PFOperator: %s", self.operator)
+        logging.info("Initialised PFOperator: %s", self.operator)
+
+class Period:
+    """
+    A class representing a period as a formal power series in z-variables and their logs.
+
+    The coefficients are stored in a dictionary of dictionaries, where the first key is the multi-index
+    of the logarithmic part and the second key is the multi-index of the z-variables. 
+    So, for example, the coefficient of
+
+        log(z0)^2 * log(z1) * z0^3 * z1^2 would be stored as coefficients[(2, 1)][(3, 2)]
+
+    """
+
+    def _initialise_ring(self):
+        z_names = ['z%d' % i for i in range(self.no_variables)]
+        log_names = ['L%d' % i for i in range(self.no_variables)]
+        ring = PolynomialRing(QQ, z_names + log_names)
+        z_gens = ring.gens()[:self.no_variables]
+        log_gens = ring.gens()[self.no_variables:]
+
+        return ring, z_gens, log_gens  # type: (PolynomialRing, list, list)
+
+    def _period_from_string(self, period_string: str) -> dict:
+        ring, z_gens, log_gens = self._initialise_ring()
+        log_of_z = dict(zip(z_gens, log_gens))
+
+        def log(zi):
+            try:
+                return log_of_z[zi]
+            except (KeyError, TypeError):
+                raise ValueError(
+                    "log(...) may only be applied to one of the z-variables z0, ..., z%d"
+                    % (self.no_variables - 1)
+                )
+
+        parse_locals = dict(ring.gens_dict())
+        parse_locals['log'] = log
+
+        try:
+            expression = ring(sage_eval(period_string, locals=parse_locals))
+        except Exception as e:
+            raise ValueError("Invalid period string: %s" % e)
+
+        coefficients = {}
+        for coeff, monomial in expression:
+            exponents = monomial.exponents()[0]
+            z_index = tuple(exponents[:self.no_variables])
+            log_index = tuple(exponents[self.no_variables:])
+            coefficients.setdefault(log_index, {})[z_index] = coeff
+
+        return coefficients
     
-    
+    def _period_to_string(self) -> str:
+        ring, z_gens, log_gens = self._initialise_ring()
+        expression = ring(0)
+        for log_index, z_dict in self.coefficients.items():
+            for z_index, coeff in z_dict.items():
+                monomial = coeff
+                for i in range(self.no_variables):
+                    monomial *= (log_gens[i] ** log_index[i]) * (z_gens[i] ** z_index[i])
+                expression += monomial
+
+        log_substitutions = {log_gens[i]: log(SR(z_gens[i])) for i in range(self.no_variables)}
+        return str(SR(expression).subs(log_substitutions))
+
+    def _max_z_degree(self) -> int:
+        # Highest total z-degree (sum of the z-multi-index) among all coefficients.
+        if not self.coefficients:
+            return 0
+        return max(
+            sum(z_index)
+            for z_dict in self.coefficients.values()
+            for z_index in z_dict
+        )
+
+    def _truncate_coefficients(self, order: int) -> dict:
+        # Drop every (log_index, z_index) entry whose total z-degree exceeds order,
+        # removing it from the dictionary rather than merely zeroing it out.
+        truncated = {}
+        for log_index, z_dict in self.coefficients.items():
+            kept = {z_index: coeff for z_index, coeff in z_dict.items() if sum(z_index) <= order}
+            if kept:
+                truncated[log_index] = kept
+        return truncated
+
+    def _apply_theta(self, coefficients: dict, index: int) -> dict:
+        """
+        Applies the logarithmic derivative theta_i = z_i * d/dz_i once to a coefficients dict of the same
+        shape as self.coefficients. It uses the product rule
+
+            theta_i(z^a log(z)^k) = a_i * z^a log(z)^k + k_i * z^a log(z)^(k - e_i).
+        """
+        result = {}
+        for log_index, z_dict in coefficients.items():
+            for z_index, coeff in z_dict.items():
+                a_i = z_index[index]
+                if a_i != 0:
+                    inner = result.setdefault(log_index, {})
+                    inner[z_index] = inner.get(z_index, 0) + a_i * coeff
+
+                k_i = log_index[index]
+                if k_i != 0:
+                    lowered_log_index = log_index[:index] + (k_i - 1,) + log_index[index + 1:]
+                    inner = result.setdefault(lowered_log_index, {})
+                    inner[z_index] = inner.get(z_index, 0) + k_i * coeff
+        return result
+
+    def apply_operator(self, pf_operator: PFOperator) -> "Period":
+        """
+        Applies a PFOperator to this period and returns the result as a new Period,
+        truncated to self.order. Each monomial of the operator is normalised as
+        coeff * z^p * theta^q (see PFOperator's docstring), so theta^q is applied
+        to the period first and the result is then multiplied by coeff * z^p.
+        """
+        if pf_operator.no_variables != self.no_variables:
+            raise ValueError(
+                "Variable count mismatch: period has %d variable(s), operator has %d."
+                % (self.no_variables, pf_operator.no_variables)
+            )
+
+        result_coefficients = {}
+        for monomial_coeff, monomial in pf_operator.operator:
+            exponents = monomial.exponents()[0]
+            z_exponents = exponents[:self.no_variables]
+            theta_exponents = exponents[self.no_variables:]
+
+            term = self.coefficients
+            for i, power in enumerate(theta_exponents):
+                for _ in range(power):
+                    term = self._apply_theta(term, i)
+
+            for log_index, z_dict in term.items():
+                inner = result_coefficients.setdefault(log_index, {})
+                for z_index, coeff in z_dict.items():
+                    shifted_z_index = tuple(z_index[i] + z_exponents[i] for i in range(self.no_variables))
+                    inner[shifted_z_index] = inner.get(shifted_z_index, 0) + monomial_coeff * coeff
+
+        result_coefficients = {
+            log_index: {z_index: c for z_index, c in z_dict.items() if c != 0}
+            for log_index, z_dict in result_coefficients.items()
+        }
+        result_coefficients = {log_index: z_dict for log_index, z_dict in result_coefficients.items() if z_dict}
+
+        return Period(
+            no_variables=self.no_variables,
+            coefficients=result_coefficients,
+            order=self.order,
+        )
+
+    def __init__(self, no_variables: int = 1, coefficients: dict = None, period_string: str = None, order: int = None):
+        self.no_variables = no_variables
+
+        # Use coefficients or period_string to initialize the period
+        if period_string is not None:
+            if coefficients is not None:
+                raise ValueError("Provide either coefficients or period_string, not both.")
+            self.coefficients = self._period_from_string(period_string)
+            logging.debug("Using string for initialisation.")
+        elif coefficients is None:
+            self.coefficients = {}
+        else:
+            self.coefficients = coefficients
+            self.period_string = self._period_to_string()
+            logging.debug("Using coefficients for initialisation.")
+
+        if order is None:
+            self.order = self._max_z_degree()
+            logging.debug("Order not provided, using maximum z-degree: %d", self.order)
+        else:
+            self.coefficients = self._truncate_coefficients(order)
+            self.order = order
+            self.period_string = self._period_to_string()
+            logging.debug("Truncated coefficients to order %d.", self.order)
+
+        logging.info("Initialised Period in %d variables at order %d.", self.no_variables, self.order)