Improve docstrings and wordings

Author: AVHopp

baybe/constraints/continuous.py

@@ -59,8 +59,8 @@ class ContinuousLinearConstraint(ContinuousConstraint):
 
     While intrapoint constraints impose conditions on each individual point of a batch,
     interpoint constraints do so **across** the points of the batch. That is, an
-    interpoint constraint of the form ``x_1 + x_2 <= 1`` enforces that the sum of all
-    ``x_1`` values plus the sum of all ``x_2`` values in the batch must not exceed 1.
+    interpoint constraint of the form ``x + y <= 1`` technically encodes
+    ``sum(x_i) + sum(y_i) <= 1`` for all points ``i`` in the batch.
     """
 
     @coefficients.validator

docs/userguide/constraints.md

@@ -87,11 +87,12 @@ A more detailed example can be found
 The constraints discussed in the previous paragraph belong to the class of so called
 "intrapoint constraints". That is, they impose conditions on each individual point of a batch.
 In contrast to this, interpoint constraints do so **across** the points of the batch.
-That is, an interpoint constraint of the form ``x_1 + x_2 <= 1`` enforces that the sum of all
-``x_1`` values plus the sum of all ``x_2`` values in the batch must not exceed 1.
+That is, an interpoint constraint of the form ``x + y <= 1`` technically encodes
+$$
+\sum_{i\text{ in batch}}x_i + \sum_{i\text{ in batch}}y_i <= 1
+$$
 A possible relevant constraint might be that only 100ml of a given solvent are available for 
-a full batch, but there is no limit for the amount of solvent to use for a single experiment
-within that batch.
+a full batch.
 
 They can be defined by using the `interpoint` keyword of the [`ContinuousLinearConstraint`](baybe.constraints.continuous.ContinuousLinearConstraint)
 class. 

examples/Constraints_Continuous/interpoint.py

@@ -3,12 +3,7 @@
 # Example for optimizing a synthetic test functions in a continuous space with linear
 # interpoint constraints.
 # While intrapoint constraints impose conditions on each individual point of a batch,
-# interpoint constraints do so **across** the points of the batch. That is, an
-# interpoint constraint of the form ``x_1 + x_2 <= 1`` enforces that the sum of all
-# ``x_1`` values plus the sum of all ``x_2`` values in the batch must not exceed 1.
-# A possible relevant constraint might be that only 100ml of a given solvent are available for
-# a full batch, but there is no limit for the amount of solvent to use for a single experiment
-# within that batch.
+# interpoint constraints do so **across** the points of the batch.
 
 # This example is a variant of the example for linear constraints, and we thus refer
 # to [`linear_constraints`](./linear_constraints.md) for more details and explanations.