ToRules[eqns] takes logical combinations of equations, in the form generated by Roots and Reduce, and converts them to lists of rules, of the form produced by Solve.

"Values for Symbols" discussed how you can use transformation rules of the form x->value to replace symbols by values. The notion of transformation rules in Mathematica is, ...

FilterRules[rules, patt] filters the list rules by picking out only those rules whose left-hand sides match patt.FilterRules[rules, {patt_1, patt_2, ...}] picks out rules ...

ArrayRules[SparseArray[...]] gives the rules {pos_1 -> val_1, pos_2 -> val_2, ...} specifying elements in a sparse array. ArrayRules[list] gives rules for SparseArray[list].

Transformation rules in Mathematica let you set local values for symbols, functions, and all other types of expressions. Using rules provides a powerful and extensible method ...

You can manipulate lists of transformation rules in Mathematica just like other symbolic expressions. It is common to assign a name to a rule or set of rules. This assigns ...

Patterns stand for classes of expressions. They contain pattern objects that represent sets of possible expressions. Pattern objects. When several pattern objects with the ...

There are a number of important interactions in Mathematica between evaluation and pattern matching. The first observation is that pattern matching is usually done on ...

Rules are a key part of Mathematica 's powerful expression transformation language. These "How tos" give step-by-step instructions for using rules in Mathematica .

ColorRules is an option for ArrayPlot which specifies how colors of cells should be determined from values.