Add expand, collect and simplify functions

Add the basic rules for `expand`, `collect` and `simplify`.

And to be honest, I am quite proud of the fact that the core code looks
_exactly_ like this (this is actual code):

```c++
    return rewrite((x+y)*z,     x*z+y*z,
                   x*(y+z),     x*y+x*z,
                   (x-y)*z,     x*z-y*z,
                   x*(y-z),     x*y-x*z);
```

A lot of template metaprogramming to turn that into transparent
building of _compile-time constants_ representing the RPL objects for
the equations, and passing that to the `rewrite` function that was
implemented earlier.

What is really neet about this is that the generated equations:

* Are automatically _shared_ if used multiple times, because they are
  represented by the same template. So the equations used in `collect`
  and those used in `expand` (which are the same in reverse) share the
  same memory.

* Automatically go into QSPI, not consuming precious flash space,
  because they are represented as initialized data arrays, and I
  requested that all C++ .rodata go in QSPI.

I intentionally did not support the historical names
(`expan` and `colct`). Our level of compatibility with the HP48 is
never going to be that good anyway.

The code as is works with `clang`, but runs into unsatisfied symbols
with g++ 10.3 due to what I believe is a g++ bug (that's what living
on the edge of template metaprogramming gives you):

```
/opt/homebrew/Cellar/arm-none-eabi-gcc/10.3-2021.07/gcc/bin/../lib/gcc/arm-none-eabi/10.3.1/../../../../arm-none-eabi/bin/ld: build/release/equation.o: in function `equation::collect() const':
equation.cc:(.text._ZNK8equation7collectEv+0xd0): undefined reference to `eq<(unsigned char)10, (unsigned char)1, (unsigned char)120, (unsigned char)10, (unsigned char)1, (unsigned char)122, (unsigned char)57, (unsigned char)10, (unsigned char)1, (unsigned char)121, (unsigned char)10, (unsigned char)1, (unsigned char)122, (unsigned char)57, (unsigned char)55>::object_data'
```

Fixes: #231

Signed-off-by: Christophe de Dinechin <christophe@dinechin.org>

fonts/EditorFont.cc

@@ -7,7 +7,7 @@ extern const unsigned char EditorFont_sparse_font_data[];
 const unsigned char EditorFont_sparse_font_data[74100] FONT_QSPI =
 {
 
-    0x81, 0x02, 0xEF, 0xC2, 0x04, 0x36, 0x00, 0x01, 0x00, 0x2C, 0x01, 0x01, 0x00, 0x00, 0x0D, 0x01,
+    0x84, 0x02, 0xEF, 0xC2, 0x04, 0x36, 0x00, 0x01, 0x00, 0x2C, 0x01, 0x01, 0x00, 0x00, 0x0D, 0x01,
     0x00, 0x2C, 0x01, 0x01, 0x08, 0x00, 0x20, 0x5F, 0x00, 0x2C, 0x01, 0x01, 0x08, 0x00, 0x02, 0x0B,
     0x05, 0x21, 0x09, 0xEF, 0xBD, 0xF7, 0xDE, 0x7B, 0xEF, 0xBD, 0xF7, 0xDE, 0x7B, 0xEF, 0xBD, 0xF7,
     0x1E, 0x00, 0x00, 0xB8, 0xFF, 0xFF, 0xFF, 0x0E, 0x03, 0x0B, 0x0B, 0x0F, 0x11, 0x8F, 0x7F, 0xFC,

fonts/HelpFont.cc

@@ -7,7 +7,7 @@ extern const unsigned char HelpFont_sparse_font_data[];
 const unsigned char HelpFont_sparse_font_data[15113] FONT_QSPI =
 {
 
-    0x81, 0x02, 0x85, 0x76, 0x14, 0x00, 0x01, 0x00, 0x11, 0x01, 0x01, 0x00, 0x00, 0x0D, 0x01, 0x00,
+    0x84, 0x02, 0x85, 0x76, 0x14, 0x00, 0x01, 0x00, 0x11, 0x01, 0x01, 0x00, 0x00, 0x0D, 0x01, 0x00,
     0x11, 0x01, 0x01, 0x03, 0x00, 0x20, 0x5F, 0x00, 0x11, 0x01, 0x01, 0x03, 0x00, 0x01, 0x04, 0x02,
     0x0D, 0x04, 0xFF, 0xFF, 0xF3, 0x03, 0x01, 0x04, 0x04, 0x05, 0x06, 0xFF, 0xFF, 0x0F, 0x01, 0x04,
     0x08, 0x0D, 0x0A, 0x12, 0x12, 0x14, 0x7F, 0x7F, 0x24, 0x24, 0x24, 0xFE, 0xFE, 0x28, 0x48, 0x48,

fonts/StackFont.cc

@@ -7,7 +7,7 @@ extern const unsigned char StackFont_sparse_font_data[];
 const unsigned char StackFont_sparse_font_data[36629] FONT_QSPI =
 {
 
-    0x81, 0x02, 0x90, 0x9E, 0x02, 0x24, 0x00, 0x01, 0x00, 0x1C, 0x01, 0x01, 0x00, 0x00, 0x0D, 0x01,
+    0x84, 0x02, 0x90, 0x9E, 0x02, 0x24, 0x00, 0x01, 0x00, 0x1C, 0x01, 0x01, 0x00, 0x00, 0x0D, 0x01,
     0x00, 0x1C, 0x01, 0x01, 0x06, 0x00, 0x20, 0x5F, 0x00, 0x1C, 0x01, 0x01, 0x06, 0x00, 0x02, 0x05,
     0x03, 0x17, 0x06, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x1F, 0xC0, 0xFF, 0x1F, 0x02, 0x05, 0x08, 0x0A,
     0x0C, 0xE7, 0xE7, 0xE7, 0xE7, 0xE7, 0xE7, 0xE7, 0xE7, 0xE7, 0xE7, 0x01, 0x05, 0x0E, 0x17, 0x10,

src/equation.cc

@@ -701,3 +701,54 @@ COMMAND_BODY(Rewrite)
 
     return OK;
 }
+
+static eq_symbol<'x'> x;
+static eq_symbol<'y'> y;
+static eq_symbol<'z'> z;
+static eq_integer<0> zero;
+static eq_integer<1> one;
+static eq_integer<2> two;
+
+equation_p equation::expand() const
+// ----------------------------------------------------------------------------
+//   Run various rewrites to expand equation
+// ----------------------------------------------------------------------------
+{
+    return rewrite((x+y)*z,     x*z+y*z,
+                   x*(y+z),     x*y+x*z,
+                   (x-y)*z,     x*z-y*z,
+                   x*(y-z),     x*y-x*z);
+}
+
+
+equation_p equation::collect() const
+// ----------------------------------------------------------------------------
+//    Run various rewrites to collect terms / factor equation
+// ----------------------------------------------------------------------------
+{
+    return rewrite(x*z+y*z,     (x+y)*z,
+                   x*y+x*z,     x*(y+z),
+                   x*z-y*z,     (x-y)*z,
+                   x*y-x*z,     x*(y-z));
+}
+
+
+equation_p equation::simplify() const
+// ----------------------------------------------------------------------------
+//   Run various rewrites to simplify equation
+// ----------------------------------------------------------------------------
+{
+    return rewrite(x + zero,    x,
+                   zero + x,    x,
+                   x - zero,    x,
+                   zero - x,    x,
+                   x * zero,    zero,
+                   zero * x,    zero,
+                   x * one,     x,
+                   one * x,     x,
+                   x / one,     x,
+                   x / x,       one,
+                   one / x,     inv(x),
+                   x * x * x,   cubed(x),
+                   x * x,       sq(x));
+}

src/equation.h

@@ -88,11 +88,34 @@ struct equation : program
     }
 
     equation_p rewrite(equation_r from, equation_r to) const;
+    equation_p rewrite(equation_p from, equation_p to) const
+    {
+        return rewrite(equation_g(from), equation_g(to));
+    }
+
     static equation_p rewrite(equation_r eq, equation_r from, equation_r to)
     {
         return eq->rewrite(from, to);
     }
 
+    template<typename from_eq, typename to_eq>
+    equation_p rewrite(from_eq from, to_eq to) const
+    {
+        return rewrite(from.as_equation(), to.as_equation());
+    }
+
+    template <typename from_eq, typename to_eq, typename ...args>
+    equation_p rewrite(from_eq from, to_eq to, args... rest) const
+    {
+        if (equation_p eq = rewrite(from, to))
+            return eq->rewrite(rest...);
+        return nullptr;
+    }
+
+    equation_p expand() const;
+    equation_p collect() const;
+    equation_p simplify() const;
+
 protected:
     static symbol_g render(uint depth, int &precedence, bool edit);
     static symbol_g parentheses(symbol_g what);

src/functions.cc

@@ -514,3 +514,51 @@ INSERT_BODY(fact)
     // We need to pass "x!' because ui.edit() strips the x
     return ui.edit(utf8("x!"), 2, ui.POSTFIX);
 }
+
+
+FUNCTION_BODY(Expand)
+// ----------------------------------------------------------------------------
+//   Expand equations
+// ----------------------------------------------------------------------------
+{
+    if (!x.Safe())
+        return nullptr;
+    if (equation_p eq = x->as<equation>())
+        return algebraic_p(eq->expand());
+    if (x->is_algebraic())
+        return x;
+    rt.type_error();
+    return nullptr;
+}
+
+
+FUNCTION_BODY(Collect)
+// ----------------------------------------------------------------------------
+//   Collect equations
+// ----------------------------------------------------------------------------
+{
+    if (!x.Safe())
+        return nullptr;
+    if (equation_p eq = x->as<equation>())
+        return algebraic_p(eq->collect());
+    if (x->is_algebraic())
+        return x;
+    rt.type_error();
+    return nullptr;
+}
+
+
+FUNCTION_BODY(Simplify)
+// ----------------------------------------------------------------------------
+//   Simplify equations
+// ----------------------------------------------------------------------------
+{
+    if (!x.Safe())
+        return nullptr;
+    if (equation_p eq = x->as<equation>())
+        return algebraic_p(eq->simplify());
+    if (x->is_algebraic())
+        return x;
+    rt.type_error();
+    return nullptr;
+}

src/functions.h

@@ -194,4 +194,8 @@ FUNCTION(im);
 FUNCTION(arg);
 FUNCTION(conj);
 
+FUNCTION(Expand);
+FUNCTION(Collect);
+FUNCTION(Simplify);
+
 #endif // FUNCTIONS_H

src/ids.tbl

@@ -236,7 +236,7 @@ CMD(re)
 CMD(im)
 CMD(arg)
 CMD(conj)
-NAMED(det, "Determinant")
+NAMED(det, "Determinant")       // Last algebraic
 
 
 
@@ -265,6 +265,9 @@ NAMED(ToList, "→List")
 CMD(Get)
 
 CMD(Rewrite)
+CMD(Expand)
+CMD(Collect)
+CMD(Simplify)
 
 NAMED(RealToComplex, "ℝ→ℂ")
 ALIAS(RealToComplex, "R→C")

src/menu.cc

@@ -537,11 +537,12 @@ MENU(SymbolicMenu,
 //   Symbolic operations
 // ----------------------------------------------------------------------------
      ID_Rewrite,
-     "Collect", ID_Unimplemented,
+     ID_Collect,
-     "Expand",  ID_Unimplemented,
+     ID_Expand,
+     ID_Simplify,
+
      "Isolate", ID_Unimplemented,
      "Apply",   ID_Unimplemented,
-     "Taylor",  ID_Unimplemented,
 
      "Ex/Co",   ID_Unimplemented,
      "→Q",      ID_Unimplemented,
@@ -554,6 +555,7 @@ MENU(SymbolicMenu,
      "∑",       ID_Unimplemented,
      "∏",       ID_Unimplemented,
      "∆",       ID_Unimplemented,
+     "Taylor",  ID_Unimplemented,
 
      "Show",    ID_Unimplemented,
      "Quote",   ID_Unimplemented,