Simplify

class pybamm.Simplification(simplified_symbols=None)

simplify(symbol)

This function recurses down the tree, applying any simplifications defined in classes derived from pybamm.Symbol. E.g. any expression multiplied by a pybamm.Scalar(0) will be simplified to a pybamm.Scalar(0). If a symbol has already been simplified, the stored value is returned.

Parameters:

• symbol (pybamm.Symbol) –
• symbol to simplify (The) –

Returns:

• pybamm.Symbol
• Simplified symbol

pybamm.simplify_if_constant(symbol)

Utility function to simplify an expression tree if it evalutes to a constant scalar, vector or matrix

pybamm.simplify_addition_subtraction(myclass, left, right)

if children are associative (addition, subtraction, etc) then try to find groups of constant children (that produce a value) and simplify them to a single term

The purpose of this function is to simplify expressions like (1 + (1 + p)), which should be simplified to (2 + p). The former expression consists of an Addition, with a left child of Scalar type, and a right child of another Addition containing a Scalar and a Parameter. For this case, this function will first flatten the expression to a list of the bottom level children (i.e. [Scalar(1), Scalar(2), Parameter(p)]), and their operators (i.e. [None, Addition, Addition]), and then combine all the constant children (i.e. Scalar(1) and Scalar(1)) to a single child (i.e. Scalar(2))

Note that this function will flatten the expression tree until a symbol is found that is not either an Addition or a Subtraction, so this function would simplify (3 - (2 + a*b*c)) to (1 + a*b*c)

This function is useful if different children expressions contain non-constant terms that prevent them from being simplified, so for example (1 + a) + (b - 2) - (6 + c) will be simplified to (-7 + a + b - c)

Parameters:

• myclass (class) – the binary operator class (pybamm.Addition or pybamm.Subtraction) operating on children left and right
• left (derived from pybamm.Symbol) – the left child of the binary operator
• right (derived from pybamm.Symbol) – the right child of the binary operator

pybamm.simplify_multiplication_division(myclass, left, right)

if children are associative (multiply, division, etc) then try to find groups of constant children (that produce a value) and simplify them

The purpose of this function is to simplify expressions of the type (1 * c / 2), which should simplify to (0.5 * c). The former expression consists of a Division, with a left child of a Multiplication containing a Scalar and a Parameter, and a right child consisting of a Scalar. For this case, this function will first flatten the expression to a list of the bottom level children on the numerator (i.e. [Scalar(1), Parameter(c)]) and their operators (i.e. [None, Multiplication]), as well as those children on the denominator (i.e. [Scalar(2)]. After this, all the constant children on the numerator and denominator (i.e. Scalar(1) and Scalar(2)) will be combined appropriately, in this case to Scalar(0.5), and combined with the nonconstant children (i.e. Parameter(c))

Note that this function will flatten the expression tree until a symbol is found that is not either an Multiplication, Division or MatrixMultiplication, so this function would simplify (3*(1 + d)*2) to (6 * (1 + d))

As well as Multiplication and Division, this function can handle MatrixMultiplication. If any MatrixMultiplications are found on the numerator/denominator, no reordering of children is done to find groups of constant children. In this case only neighbouring constant children on the numerator are simplified

Parameters:

• myclass (class) – the binary operator class (pybamm.Addition or pybamm.Subtraction) operating on children left and right
• left (derived from pybamm.Symbol) – the left child of the binary operator
• right (derived from pybamm.Symbol) – the right child of the binary operator