Definition

An instance f of the data type Slp is an SLP with type SLP and a representation which contains the following information :

• Operator. This is one of NOP_FE,NOP_VAR,ADD,SUB, MULT, DIV, EXP, DIFF. The NOP_FE operator implies that the Slp has no operator, i.e. is a leaf in the d.a.g., representing a number. The NOP_VAR operator also represents a leaf node, but containing a variable. The EXP operator corresponds to the operation ^, that is, the operation (n of type int ) is represented by an EXP node with left child the Slp node corresponding to a and right child a node corresponding to the integer value n . The DIFF operator will be explained below.
• Pointers to the Slp's for the left and right child (i.e. the operands).
• Pointer to a Field_element which stores the current value of the node after an evaluation.
• An int value which represents the the last time the node was evaluated. This is compared to the global value Slp::Eval_level to check if the value is current.
• An array of derivatives of the Slp node w.r.t. the variables over which the Slp is defined.
• An array of int flags which indicate which derivatives have been computed.
• The anti-derivative of the current Slp (required for avoiding exponential growth during the differentiation process)
• An int representing the degree of the Slp in a given variable.
• An int value representing the last time the degree was evaluated. (This works similar to the evaluation process described above, except we are interested in computing the degree of the Slp in a given variable.)