diff --git a/doc/userdoc.org b/doc/userdoc.org
index d356b4df2ac60b8f592d3008746a21b8ce9eb020..1eaa03f39e54ff95f6d0ed0371f188bfb2f3c7ff 100644
--- a/doc/userdoc.org
+++ b/doc/userdoc.org
@@ -712,7 +712,7 @@ The interpreter gives type to some special expressions.
| ~\r~ | carriage return |
| ~\t~ | horizontal tab |
| ~\v~ | vertical tab |
- These special character are not interpreted by ~pugs~ itself but
+ These special characters are not interpreted by ~pugs~ itself but
interpreted by the system when an output is created. They are just
allowed in the definition of a ~string~.
@@ -830,43 +830,43 @@ lists are sorted by type of left hand side variable.
- ~B~: boolean left hand side variable. One is only allowed to affect boolean
values.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ (for convenience) |
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
- ~R~: real ($\mathbb{R}$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
- | ~R~ |
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
- | ~R~ |
- | ~R^1~ |
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1~ |
- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
- | allowed expression type |
+ | ~=~ allowed expression type |
|---------------------------------------------|
| ~R^2~ |
| ~0~ (special value) |
@@ -891,9 +891,9 @@ lists are sorted by type of left hand side variable.
#+results: R2-invalid-integer-affectation
- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
- | allowed expression type |
+ | ~=~ allowed expression type |
|---------------------------------------------|
- | ~R^3~ |
+ | ~R^3~ |
| ~0~ (special value) |
| list of 3 scalar (~B~, ~N~, ~Z~ or ~R~) expressions |
An example of initialization using a list is
@@ -907,17 +907,17 @@ lists are sorted by type of left hand side variable.
the output is
#+RESULTS: affectation-to-R3-from-list
-- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^1\times1$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
- | ~R~ |
- | ~R^1x1~ |
-
-- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^2x2$) left hand side variable.
- | allowed expression type |
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^{1\times1}$) left hand side variable.
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1x1~ |
+
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^{2\times2}$) left hand side variable.
+ | ~=~ allowed expression type |
|---------------------------------------------|
| ~R^2x2~ |
| ~0~ (special value) |
@@ -934,8 +934,8 @@ lists are sorted by type of left hand side variable.
which produces
#+RESULTS: affectation-to-R2x2-from-list
-- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^3x3$) left hand side variable.
- | allowed expression type |
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^{3\times3}$) left hand side variable.
+ | ~=~ allowed expression type |
|---------------------------------------------|
| ~R^3x3~ |
| ~0~ (special value) |
@@ -955,19 +955,19 @@ lists are sorted by type of left hand side variable.
- ~string~ left hand side variable. Expressions of any basic types can
be used as the right hand side.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
- | ~R~ |
- | ~R^1~ |
- | ~R^2~ |
- | ~R^3~ |
- | ~R^1x1~ |
- | ~R^2x2~ |
- | ~R^3x3~ |
- | ~string~ |
+ | ~=~ allowed expression type |
+ |---------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1~ |
+ | ~R^2~ |
+ | ~R^3~ |
+ | ~R^1x1~ |
+ | ~R^2x2~ |
+ | ~R^3x3~ |
+ | ~string~ |
***** List of defined operator ~+=~ for basic types.
@@ -975,85 +975,289 @@ lists are sorted by type of left hand side variable.
variables.
- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ (for convenience) |
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
- ~R~: real ($\mathbb{R}$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
- | ~R~ |
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~R^1~ |
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~R^1~ |
- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
- | allowed expression type |
- |---------------------------------------------|
- | ~R^2~ |
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~R^2~ |
- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
- | allowed expression type |
- |---------------------------------------------|
- | ~R^3~ |
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~R^3~ |
-- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^1\times1$) left hand side variable.
- | allowed expression type |
- |-------------------------|
- | ~R^1x1~ |
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^{1\times1}$) left hand side variable.
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~R^1x1~ |
-- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^2x2$) left hand side variable.
- | allowed expression type |
- |---------------------------------------------|
- | ~R^2x2~ |
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^{2\times2}$) left hand side variable.
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~R^2x2~ |
-- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^3x3$) left hand side variable.
- | allowed expression type |
- |---------------------------------------------|
- | ~R^3x3~ |
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^{3\times3}$) left hand side variable.
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~R^3x3~ |
- ~string~ left hand side variable. Expressions of any basic types can
be used as the right hand side.
- | allowed expression type |
- |-------------------------|
- | ~B~ |
- | ~N~ |
- | ~Z~ |
- | ~R~ |
- | ~R^1~ |
- | ~R^2~ |
- | ~R^3~ |
- | ~R^1x1~ |
- | ~R^2x2~ |
- | ~R^3x3~ |
- | ~string~ |
-
-***** TODO List of defined operator ~-=~ for basic types.
+ | ~+=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+ | ~R^1~ |
+ | ~R^2~ |
+ | ~R^3~ |
+ | ~R^1x1~ |
+ | ~R^2x2~ |
+ | ~R^3x3~ |
+ | ~string~ |
+
+***** List of defined operator ~-=~ for basic types.
- ~B~: the ~-=~ operator is not defined for left hand side boolean variables.
-***** TODO List of defined operator ~*=~ for basic types.
+- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
+
+- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+
+- ~R~: real ($\mathbb{R}$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~R^1~ |
+
+- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~R^2~ |
+
+- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~R^3~ |
+
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^{1\times1}$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~R^1x1~ |
+
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^{2\times2}$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~R^2x2~ |
+
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^{3\times3}$) left hand side variable.
+ | ~-=~ allowed expression type |
+ |----------------------------|
+ | ~R^3x3~ |
+
+- ~string~: the ~-=~ operator is not defined for left hand side string variables.
+
+***** List of defined operator ~*=~ for basic types.
- ~B~: the ~*=~ operator is not defined for left hand side boolean variables.
-***** TODO List of defined operator ~/=~ for basic types.
+- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
+
+- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+
+- ~R~: real ($\mathbb{R}$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^{1\times1}$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^{2\times2}$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^{3\times3}$) left hand side variable.
+ | ~*=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+#+BEGIN_note
+Observe that for these small matrix types ($\mathbb{R}^{d\times d}$) the
+construction ~A *= B;~ is not allowed. The main reason for that is that
+for $d>1$ this operation has no interests since it requires a
+temporary. One will see bellow that one can write ~A = A*B;~ if needed.
+#+END_note
+
+- ~string~: the ~*=~ operator is not defined for left hand side string variables.
+
+***** List of defined operator ~/=~ for basic types.
- ~B~: the ~/=~ operator is not defined for left hand side boolean variables.
+- ~N~: natural integer ($\mathbb{N}$ or $\mathbb{Z}_{\ge0}$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ (for convenience) |
+
+- ~Z~: integer ($\mathbb{Z}$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+
+- ~R~: real ($\mathbb{R}$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1~: vector of dimension 1 ($\mathbb{R}^1$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^2~: vector of dimension 2 ($\mathbb{R}^2$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^3~: vector of dimension 3 ($\mathbb{R}^3$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^1x1~: matrix of dimensions $1\times1$ ($\mathbb{R}^{1\times1}$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^2x2~: matrix of dimension $2\times2$ ($\mathbb{R}^{2\times2}$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+- ~R^3x3~: matrix of dimension $3\times3$ ($\mathbb{R}^{3\times3}$) left hand side variable.
+ | ~/=~ allowed expression type |
+ |----------------------------|
+ | ~B~ |
+ | ~N~ |
+ | ~Z~ |
+ | ~R~ |
+
+
**** Unary operators
The ~pugs~ language allows the following tokens as unary operators