Incorporate decapodes ACSet serialization (#600)

- First pass on extracting and serializing the Decapodes ACSet
representation.
   - Includes working example of Halfar dome PDE.
- Math Expression handles Gradient and Absolute value explicitly.
- Math Expression explicitly incorporates multiplication operations for
consecutive Mrows, and handles equals operators.
- Minor bug fixes and insertion of asserts.

---------

Co-authored-by: Deepsana Shahi <[email protected]>
Co-authored-by: ualiangzhang <[email protected]>
Co-authored-by: Justin <[email protected]>

skema/skema-rs/mathml/src/ast.rs

@@ -66,6 +66,7 @@ pub enum MathExpression {
     //GroupTuple(Vec<MathExpression>),
     Ci(Ci),
     Differential(Differential),
+    AbsoluteSup(Box<MathExpression>, Box<MathExpression>),
     //Differential(Box<MathExpression>, Box<MathExpression>),
     #[default]
     None,
@@ -97,9 +98,13 @@ impl fmt::Display for MathExpression {
                 Ok(())
             }
             MathExpression::Differential(Differential { diff, func }) => {
-                write!(f, "{diff}");
+                write!(f, "{diff}")?;
                 write!(f, "{func}")
             }
+            MathExpression::AbsoluteSup(base, superscript) => {
+                write!(f, "{:?}", base)?;
+                write!(f, "{superscript:?}")
+            }
             expression => write!(f, "{expression:?}"),
         }
     }

skema/skema-rs/mathml/src/ast/operator.rs

@@ -27,6 +27,8 @@ pub enum Operator {
     Comma,
     Grad,
     Dot,
+    Div,
+    Abs,
     Derivative(Derivative),
     Sin,
     Cos,
@@ -64,7 +66,7 @@ impl fmt::Display for Operator {
                 var_index,
                 bound_var,
             }) => {
-                write!(f, "D({order}, {var_index}, {bound_var})")
+                write!(f, "D({order}, {bound_var})")
             }
             Operator::Exp => write!(f, "exp"),
             Operator::Power => write!(f, "^"),
@@ -84,6 +86,8 @@ impl fmt::Display for Operator {
             Operator::Mean => write!(f, "Mean"),
             Operator::Grad => write!(f, "Grad"),
             Operator::Dot => write!(f, "Dot"),
+            Operator::Div => write!(f, "Div"),
+            Operator::Abs => write!(f, "Abs"),
         }
     }
 }

skema/skema-rs/mathml/src/parsers.rs

@@ -1,3 +1,4 @@
+pub mod decapodes_serialization;
 pub mod first_order_ode;
 pub mod generic_mathml;
 pub mod interpreted_mathml;