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authorMichael Schneeberger <michael.schneeberger@fhnw.ch>2023-09-05 11:25:35 +0200
committerMichael Schneeberger <michael.schneeberger@fhnw.ch>2023-09-05 11:25:35 +0200
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@@ -1,6 +1,6 @@
# Multivariate polynomial library
-`polymatrix` is a library to represent and operate on multivariate polynomials.
+`polymatrix` is a library to represent and operate on multivariate polynomial matrices.
It is used to define Sum Of Squares optimization problems.
@@ -16,11 +16,11 @@ Some aspects of the library:
* [`polymatrix.v_stack`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/__init__.py)
* [`polymatrix.block_diag`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/__init__.py).
* polynomial expressions are manipulated using methods like
- * [`diff`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/mixins/expressionmixin.py),
- * [`reshape`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/mixins/expressionmixin.py)
- * [`substitute`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/mixins/expressionmixin.py)
- * [`sum`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/mixins/expressionmixin.py)
- * [`to_constant`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/mixins/expressionmixin.py)
+ * [`diff`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/expression.py),
+ * [`reshape`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/expression.py)
+ * [`substitute`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/expression.py)
+ * [`sum`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/expression.py)
+ * [`to_constant`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/expression.py)
* an expression is converted to matrix representation using [`polymatrix.to_matrix_repr`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/__init__.py). To get the actual representation, the [`apply(state)`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/statemonad/mixins/statemonadmixin.py) method needs to be called.
## Example
@@ -31,7 +31,7 @@ f_1(x_1, x_2) = x_1 + x_2
f_2(x_1, x_2) = x_1 + x_1 x_2
-Then, the two expression are combined using the [`__add__`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/mixins/expressionmixin.py) (or equivalently `+` infix) method
+Then, the two expression are combined using the [`__add__`](https://gitlab.nccr-automation.ch/michael.schneeberger/polymatrix/-/blob/main/polymatrix/expression/expression.py) (or equivalently `+` infix) method
f_3(x_1, x_2) = f_1(x_1, x_2) + f_2(x_1, x_2) = 2 x_1 + x_2 + x_1 x_2