many edits

quarto/alternatives/symbolics.qmd

@@ -501,10 +501,11 @@ d, r = polynomial_coeffs(ex, (x,))
 r
 ```
 
-To find the degree of a monomial expression, the `degree` function is available. Here it is applied to each monomial in `d`:
+To find the degree of a monomial expression, the `degree` function is available, though not exported. Here it is applied to each monomial in `d`:
 
 
 ```{julia}
+import Symbolics: degree
 [degree(k) for (k,v) ∈ d]
 ```
 
@@ -773,6 +774,11 @@ Symbolics.jacobian(eqs, [x,y])
 
 ### Integration
 
+::: {.callout-note}
+#### This area is very much WIP
+
+The use of `SymbolicNumericIntegration` below is currently broken.
+:::
 
 The `SymbolicNumericIntegration` package provides a means to integrate *univariate* expressions through its `integrate` function.
 
@@ -904,18 +910,27 @@ v = factor_rational(u)
 
 As such, the integrals have numeric differences from their mathematical counterparts:
 
+::: {.callout-note}
+#### Errors ahead
+
+These last commands are note being executed, as there are errors.
+:::
+
 
 ```{julia}
-a,b,c = integrate(u)
+#| eval: false
+a,b,c = integrate(u)   # not
 ```
 
 We can see a bit of how much through the following, which needs a tolerance set to identify the rational numbers of the mathematical factorization correctly:
 
 
 ```{julia}
+#| eval: false
 cs = [first(arguments(term)) for term ∈ arguments(a)] # pick off coefficients
 ```
 
 ```{julia}
-rationalize.(cs; tol=1e-8)
+#| eval: false
+rationalize.(cs[2:end]; tol=1e-8)
 ```