Issue #1199: add in texput rules to display root(x,n) as surd.

doc/en/Authoring/Options.md

@@ -113,6 +113,8 @@ Do you really want to continue using \(\sqrt{}\) in your teaching?  In his *Elem
 
 A lot of elementary mathematics involves converting from one form to another and back again.  Sometimes these forms have important differences of use, e.g. factored form or completed square form for a quadratic.  However, sometimes these equivalent forms are more customary than because it *"manifestly corresponds with the nature of the thing"* in question.  I digress...
 
+STACK defines an \(n\)th root function `root(x,n)` which is a noun form for \(\sqrt[n](x)\).  This can be used by students, but if teachers wish to use this in question variables etc. then they must prefix this with the apostophie to create the nounform `'root(x,n)` to prevent immediate evaluation to `x^(1/n)`.
+
 ### sqrt(-1) {#sqrt_minus_one} ###
 
 In Maxima `%i` is the complex unit satisfying `%i^2=-1`.  However, students would

stack/cas/security-map.json

@@ -6708,7 +6708,12 @@
       "globalyforbiddenfunction": true
   },
   "root": {
-      "function": "s"
+      "function": "s",
+      "nounfunction": "'root"
+  },
+  "'root": {
+      "function": "t",
+      "nounfunctionfor": "root"
   },
   "rootsconmode": {
       "variable": "s"

stack/maxima/assessment.mac

@@ -365,6 +365,10 @@ root([ex]) := block(
   if length(ex) = 1 then return(sqrt(first(ex))),
   if length(ex) = 2 then return(first(ex)^(1/second(ex)))
 )$
+texroot(ex) := if is(length(args(ex))=1) then concat("\\sqrt{", tex1(first(args(ex))), "}") else concat("\\sqrt[", tex1(second(args(ex))), "]{", tex1(first(args(ex))), "}")$
+texput(nounify(root), texroot)$
+texput(verbify(root), texroot)$
+
 
 /* Denominators of fractions should not contain sqrt, root, %i or fractional powers. */
 rational_fail(ex) := block(

tests/fixtures/answertestfixtures.class.php

@@ -114,6 +114,9 @@ class stack_answertest_test_data {
 
         ['AlgEquiv', '', 'x^(1/2)', 'sqrt(x)', 1, '', 'Powers and roots'],
         ['AlgEquiv', '', 'x', 'sqrt(x^2)', 0, '', ''],
+        ['AlgEquiv', '', '\'root(x)', 'x^(1/2)', 1, '', ''],
+        ['AlgEquiv', '', '\'root(x,m)', 'x^(1/m)', 1, '', ''],
+        ['AlgEquiv', '', 'x', '\'root(x^2)', 0, '', ''],
         ['AlgEquiv', '', 'abs(x)', 'sqrt(x^2)', 1, '', ''],
         ['AlgEquiv', '', '1/abs(x)^(1/3)', '(abs(x)^(1/3)/abs(x))^(1/2)', 1, '', ''],
         ['AlgEquiv', '', 'sqrt((x-3)*(x-5))', 'sqrt(x-3)*sqrt(x-5)', 0, '', ''],

tests/fixtures/inputfixtures.class.php

@@ -459,8 +459,8 @@ function at a point \(f(x)\).  Maybe a 'gocha' for the question author....",
             "There is an option to display this as \(x^{1/2}|\).",
         ],
         ['root(x)', 'php_true', 'root(x)', 'cas_true', '\sqrt{x}', '', ''],
-        ['root(x,3)', 'php_true', 'root(x,3)', 'cas_true', 'x^{\frac{1}{3}}', '', ''],
-        ['root(2,-3)', 'php_true', 'root(2,-3)', 'cas_true', '2^{\frac{1}{-3}}', '', ''],
+        ['root(x,3)', 'php_true', 'root(x,3)', 'cas_true', '\sqrt[3]{x}', '', ''],
+        ['root(2,-3)', 'php_true', 'root(2,-3)', 'cas_true', '\sqrt[-3]{2}', '', ''],
         // Parser rules in 4.3, identify cases where known functions (cf) are prefixed with single letter variables.
         ['bsin(t)', 'php_true', 'b*sin(t)', 'cas_true', 'b\cdot \sin \left( t \right)', 'missing_stars', ""],
         // So we have added gcf as a function so it is not g*cf...

tests/input_algebraic_test.php

@@ -1555,6 +1555,22 @@ public function test_validate_student_response_realsets_sametype_ok() {
                 '\[ \left( a,\, b\right] \]');
     }
 
+    public function test_validate_student_response_root() {
+        $options = new stack_options();
+        $el = stack_input_factory::make('algebraic', 'sans1', 'x^(1/n)');
+        $el->set_parameter('sameType', true);
+
+        // We don't require intervals to have real numbers in them.
+        $state = $el->validate_student_response(['sans1' => 'root(x,n)'], $options, 'x^(1/n)',
+            new stack_cas_security(false, '', '', ['ta']));
+        $this->assertEquals($state->status, stack_input::VALID);
+        $this->assertEquals('', $state->note);
+        $this->assertEquals('', $state->errors);
+        $this->assertEquals($state->contentsmodified, '\'root(x,n)');
+        $this->assertEquals($state->contentsdisplayed,
+            '\[ \sqrt[n]{x} \]');
+    }
+
     public function test_validate_student_response_tex() {
         $options = new stack_options();
         $el = stack_input_factory::make('algebraic', 'sans1', '{}');