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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en">
	<head>
		<title>TeXmacs Maxima Integrals</title>
		<link rel="stylesheet" href="/oldstyle.css" />
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		<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
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		<meta charset="utf-8" />
	</head>
	<body>
		<h1>TeXmacs Maxima Integrals</h1>
		
		<p>
		I've been trying to get <a href="https://www.texmacs.org/">TeXmacs</a> with its <a href="https://maxima.sourceforge.io/">Maxima</a> <a href="https://www.texmacs.org/tmweb/documents/tutorials/maxima-tutorial/maxima-tutorial.en.html">plugin</a> to work.
		</p>
		<p>
		Enabling the "mathematical input" mode in its interactive sessions I can use TeXmacs as a nice computer algebra system. However, an issue arises when I use integration.
		</p>
		<p>
		If I enter \(\displaystyle\int x\,\mathrm{d}\,x\) with "<code>\int &lt;enter&gt;x d&lt;tab&gt;&lt;tab&gt;x</code>" (spaces here are actually typed in while the "<code>&lt;tab&gt;</code>"s and "<code>&lt;enter&gt;</code>"s are their respective keys), I get this idiosyncratic error:
		</p>
		<pre>incorrect syntax: 1 is not an infix operator
integrate( x 1,
	     ^</pre>
		<p>
		This seems to be a bug when TeXmacs is translating things into Maxima. Just replace the "<code>&lt;tab&gt;</code>" between the integrand and the "\(\mathrm{d}\)" with a multiplication operator entered by "<code>*</code>". For example, <code>\int &lt;enter&gt;x*d&lt;tab&gt;&lt;tab&gt;x</code> yields the correct result of \(\displaystyle\frac{x^2}{2}\) rather than the nonsensical error.
		</p>
		<p>
		For reference, the source code of a demonstration document is included below in Scheme and XML-like (?) formats.
		</p>
		<pre>(document (TeXmacs "2.1.1") (style (tuple "generic" "maxima")) (body (document (session "maxima" "default" (document (unfolded-io-math (document (with "color" "red" (concat "(" (with "math-font-family" "rm" "%i") "8) "))) (document (concat (big "int") " x <mathd> x")) (document "" "incorrect syntax: 1 is not an infix operator" "integrate( x 1," "             ^")) (unfolded-io-math (document (with "color" "red" (concat "(" (with "math-font-family" "rm" "%i") "8) "))) (document (concat (big "int") "x*<mathd> x")) (document "" (concat " " (math (with "math-display" "true" (concat (text (with "font-family" "tt" "color" "red" (concat "(" (with "math-font-family" "rm" "%o8") ") "))) (frac (concat "x" (rsup "2")) "2"))))))))))) (initial (collection (associate "page-medium" "paper") (associate "preamble" "true") (associate "prog-scripts" "maxima"))))</pre>
		<pre>&lt;TeXmacs|2.1.1&gt;

&lt;style|&lt;tuple|generic|maxima&gt;&gt;

&lt;\body&gt;
  &lt;\session|maxima|default&gt;
    &lt;\unfolded-io-math&gt;
      &lt;with|color|red|(&lt;with|math-font-family|rm|%i&gt;8) &gt;
    &lt;|unfolded-io-math&gt;
      &lt;big|int&gt; x \&lt;mathd\&gt; x
    &lt;|unfolded-io-math&gt;
      \;

      incorrect syntax: 1 is not an infix operator

      integrate( x 1,

      \ \ \ \ \ \ \ \ \ \ \ \ \ ^
    &lt;/unfolded-io-math&gt;

    &lt;\unfolded-io-math&gt;
      &lt;with|color|red|(&lt;with|math-font-family|rm|%i&gt;8) &gt;
    &lt;|unfolded-io-math&gt;
      &lt;big|int&gt;x*\&lt;mathd\&gt; x
    &lt;|unfolded-io-math&gt;
      \;

      \ &lt;math|&lt;with|math-display|true|&lt;text|&lt;with|font-family|tt|color|red|(&lt;with|math-font-family|rm|%o8&gt;)
      &gt;&gt;&lt;frac|x&lt;rsup|2&gt;|2&gt;&gt;&gt;
    &lt;/unfolded-io-math&gt;
  &lt;/session&gt;
&lt;/body&gt;

&lt;\initial&gt;
  &lt;\collection&gt;
    &lt;associate|page-medium|paper&gt;
    &lt;associate|preamble|false&gt;
    &lt;associate|prog-scripts|maxima&gt;
  &lt;/collection&gt;
&lt;/initial&gt;</pre>
		<div id="footer">
			<hr />
			<p><a href="/">Runxi Yu's Website</a></p>
			
		</div>
	</body>
</html>
generated by cgit-pink 1.4.1-2-gfad0 (git 2.36.2.497.gbbea4dcf42) at 2024-11-25 02:58:41 +0000
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//: The goal of layers is to make programs more easy to understand and more
//: malleable, easy to rewrite in radical ways without accidentally breaking
//: some corner case. Tests further both goals. They help understandability by
//: letting one make small changes and get feedback. What if I wrote this line
//: like so? What if I removed this function call, is it really necessary?
//: Just try it, see if the tests pass. Want to explore rewriting this bit in
//: this way? Tests put many refactorings on a firmer footing.
//:
//: But the usual way we write tests seems incomplete. Refactorings tend to
//: work in the small, but don't help with changes to function boundaries. If
//: you want to extract a new function you have to manually test-drive it to
//: create tests for it. If you want to inline a function its tests are no
//: longer valid. In both cases you end up having to reorganize code as well as
//: tests, an error-prone activity.
//:
//: In response, this layer introduces the notion of domain-driven *white-box*
//: testing. We focus on the domain of inputs the whole program needs to
//: handle rather than the correctness of individual functions. All white-box
//: tests invoke the program in a single way: by calling run() with some
//: input. As the program operates on the input, it traces out a list of
//: _facts_ deduced about the domain:
//:   trace("label") << "fact 1: " << val;
//:
//: Tests can now check for these facts in the trace:
//:   CHECK_TRACE_CONTENTS("label", "fact 1: 34\n"
//:                                 "fact 2: 35\n");
//:
//: Since we never call anything but the run() function directly, we never have
//: to rewrite the tests when we reorganize the internals of the program. We
//: just have to make sure our rewrite deduces the same facts about the domain,
//: and that's something we're going to have to do anyway.
//:
//: To avoid the combinatorial explosion of integration tests, each layer
//: mainly logs facts to the trace with a common *label*. All tests in a layer
//: tend to check facts with this label. Validating the facts logged with a
//: specific label is like calling functions of that layer directly.
//:
//: To build robust tests, trace facts about your domain rather than details of
//: how you computed them.
//:
//: More details: http://akkartik.name/blog/tracing-tests
//:
//: ---
//:
//: Between layers and domain-driven testing, programming starts to look like a
//: fundamentally different activity. Instead of focusing on a) superficial,
//: b) local rules on c) code [like say http://blog.bbv.ch/2013/06/05/clean-code-cheat-sheet],
//: we allow programmers to engage with the a) deep, b) global structure of
//: the c) domain. If you can systematically track discontinuities in the
//: domain, you don't care if the code used gotos as long as it passed all
//: tests. If tests become more robust to run, it becomes easier to try out
//: radically different implementations for the same program. If code is
//: super-easy to rewrite, it becomes less important what indentation style it
//: uses, or that the objects are appropriately encapsulated, or that the
//: functions are referentially transparent.
//:
//: Instead of plumbing, programming becomes building and gradually refining a
//: map of the environment the program must operate under. Whether a program
//: is 'correct' at a given point in time is a red herring; what matters is
//: avoiding regression by monotonically nailing down the more 'eventful'
//: parts of the terrain. It helps readers new and old, and rewards curiosity,
//: to organize large programs in self-similar hierarchies of example tests
//: colocated with the code that makes them work.
//:
//:   "Programming properly should be regarded as an activity by which
//:   programmers form a mental model, rather than as production of a program."
//:   -- Peter Naur (http://alistair.cockburn.us/ASD+book+extract%3A+%22Naur,+Ehn,+Musashi%22)

//:: == Core data structures

:(before "End Globals")
trace_stream* Trace_stream = NULL;

:(before "End Types")
struct trace_stream {
  vector<trace_line> past_lines;
  // End trace_stream Fields

  trace_stream() {
    // End trace_stream Constructor
  }
  ~trace_stream() {
    // End trace_stream Destructor
  }
  // End trace_stream Methods
};

//:: == Adding to the trace

//: Top-level method is trace() which can be used like an ostream. Usage:
//:   trace(depth, label) << ... << end();
//: Don't forget the 'end()' to actually append to the trace.
:(before "End Includes")
// No brackets around the expansion so that it prints nothing if Trace_stream
// isn't initialized.
#define trace(...)  !Trace_stream ? cerr : Trace_stream->stream(__VA_ARGS__)

:(before "End trace_stream Fields")
// accumulator for current trace_line
ostringstream* curr_stream;
string curr_label;
int curr_depth;
// other stuff
int collect_depth;  // avoid tracing lower levels for speed
ofstream null_stream;  // never opened, so writes to it silently fail

//: Some constants.
:(before "struct trace_stream")  // include constants in all cleaved compilation units
const int Max_depth = 9999;
:(before "End trace_stream Constructor")
curr_stream = NULL;
curr_depth = Max_depth;
collect_depth = Max_depth;

:(before "struct trace_stream")
struct trace_line {
  string contents;
  string label;
  int depth;  // 0 is 'sea level'; positive integers are progressively 'deeper' and lower level
  trace_line(string c, string l) {
    contents = c;
    label = l;
    depth = 0;
  }
  trace_line(string c, string l, int d) {
    contents = c;
    label = l;
    depth = d;
  }
};

//: Starting a new trace line.
:(before "End trace_stream Methods")
ostream& stream(string label) {
  return stream(Max_depth, label);
}

ostream& stream(int depth, string label) {
  if (depth > collect_depth) return null_stream;
  curr_stream = new ostringstream;
  curr_label = label;
  curr_depth = depth;
  return *curr_stream;
}

//: End of a trace line; append it to the trace.
:(before "End Types")
struct end {};
:(code)
ostream& operator<<(ostream& os, end /*unused*/) {
  if (Trace_stream) Trace_stream->newline();
  return os;
}

:(before "End trace_stream Methods")
void newline();
:(code)
void trace_stream::newline() {
  if (!curr_stream) return;
  string curr_contents = curr_stream->str();
  if (!curr_contents.empty()) {
    past_lines.push_back(trace_line(curr_contents, trim(curr_label), curr_depth));  // preserve indent in contents
    // maybe incrementally dump trace
    trace_line& t = past_lines.back();
    if (should_incrementally_print_trace()) {
      cerr       << std::setw(4) << t.depth << ' ' << t.label << ": " << t.contents << '\n';
    }
    // End trace Commit
  }

  // clean up
  delete curr_stream;
  curr_stream = NULL;
  curr_label.clear();
  curr_depth = Max_depth;
}

//:: == Initializing the trace in tests

:(before "End Includes")
#define START_TRACING_UNTIL_END_OF_SCOPE  lease_tracer leased_tracer;
:(before "End Test Setup")
START_TRACING_UNTIL_END_OF_SCOPE

//: Trace_stream is a resource, lease_tracer uses RAII to manage it.
:(before "End Types")
struct lease_tracer {
  lease_tracer();
  ~lease_tracer();
};
:(code)
lease_tracer::lease_tracer() { Trace_stream = new trace_stream; }
lease_tracer::~lease_tracer() {
  delete Trace_stream;
  Trace_stream = NULL;
}

//:: == Errors using traces

:(before "End Includes")
#define raise  (!Trace_stream ? (scroll_to_bottom_and_close_console(),++Trace_errors,cerr) /*do print*/ : Trace_stream->stream(Error_depth, "error"))

//: Print errors to the screen by default.
:(before "struct trace_stream")  // include constants in all cleaved compilation units
const int Error_depth = 0;
:(before "End Globals")
int Hide_errors = false;  // if set, don't print errors to screen
:(before "End Reset")
Hide_errors = false;
:(code)
bool trace_stream::should_incrementally_print_trace() {
  if (!Hide_errors && curr_depth == Error_depth) return true;
  // End Incremental Trace Print Conditions
  return false;
}
:(before "End trace_stream Methods")
bool should_incrementally_print_trace();

:(before "End Globals")
int Trace_errors = 0;  // used only when Trace_stream is NULL

// Fail tests that displayed (unexpected) errors.
// Expected errors should always be hidden and silently checked for.
:(before "End Test Teardown")
if (Passed && !Hide_errors && trace_contains_errors()) {
  Passed = false;
}
:(code)
bool trace_contains_errors() {
  return Trace_errors > 0 || trace_count("error") > 0;
}

:(before "End Includes")
// If we aren't yet sure how to deal with some corner case, use assert_for_now
// to indicate that it isn't an inviolable invariant.
#define assert_for_now assert
#define raise_for_now raise

//: Automatically close the console in some situations.
:(before "End One-time Setup")
atexit(scroll_to_bottom_and_close_console);
:(code)
void scroll_to_bottom_and_close_console() {
  if (!tb_is_active()) return;
  // leave the screen in a relatively clean state
  tb_set_cursor(tb_width()-1, tb_height()-1);
  cout << "\r\n";
  tb_shutdown();
}
:(before "End Includes")
#include "termbox/termbox.h"

//:: == Other assertions on traces
//: Primitives:
//:   - CHECK_TRACE_CONTENTS(lines)
//:     Assert that the trace contains the given lines (separated by newlines)
//:     in order. There can be other intervening lines between them.
//:   - CHECK_TRACE_DOESNT_CONTAIN(line)
//:   - CHECK_TRACE_DOESNT_CONTAIN(label, contents)
//:     Assert that the trace doesn't contain the given (single) line.
//:   - CHECK_TRACE_COUNT(label, count)
//:     Assert that the trace contains exactly 'count' lines with the given
//:     'label'.
//:   - CHECK_TRACE_CONTAINS_ERRORS()
//:   - CHECK_TRACE_DOESNT_CONTAIN_ERRORS()
//:   - trace_count_prefix(label, prefix)
//:     Count the number of trace lines with the given 'label' that start with
//:     the given 'prefix'.

:(before "End Includes")
#define CHECK_TRACE_CONTENTS(...)  check_trace_contents(__FUNCTION__, __FILE__, __LINE__, __VA_ARGS__)

#define CHECK_TRACE_DOESNT_CONTAIN(...)  CHECK(trace_doesnt_contain(__VA_ARGS__))

#define CHECK_TRACE_COUNT(label, count) \
  if (Passed && trace_count(label) != (count)) { \
    cerr << "\nF - " << __FUNCTION__ << "(" << __FILE__ << ":" << __LINE__ << "): trace_count of " << label << " should be " << count << '\n'; \
    cerr << "  got " << trace_count(label) << '\n';  /* multiple eval */ \
    DUMP(label); \
    Passed = false; \
    return;  /* Currently we stop at the very first failure. */ \
  }

#define CHECK_TRACE_CONTAINS_ERRORS()  CHECK(trace_contains_errors())
#define CHECK_TRACE_DOESNT_CONTAIN_ERRORS() \
  if (Passed && trace_contains_errors()) { \
    cerr << "\nF - " << __FUNCTION__ << "(" << __FILE__ << ":" << __LINE__ << "): unexpected errors\n"; \
    DUMP("error"); \
    Passed = false; \
    return; \
  }

// Allow tests to ignore trace lines generated during setup.
#define CLEAR_TRACE  delete Trace_stream, Trace_stream = new trace_stream

:(code)
bool check_trace_contents(string FUNCTION, string FILE, int LINE, string expected) {
  if (!Passed) return false;
  if (!Trace_stream) return false;
  vector<string> expected_lines = split(expected, "\n");
  int curr_expected_line = 0;
  while (curr_expected_line < SIZE(expected_lines) && expected_lines.at(curr_expected_line).empty())
    ++curr_expected_line;
  if (curr_expected_line == SIZE(expected_lines)) return true;
  string label, contents;
  split_label_contents(expected_lines.at(curr_expected_line), &label, &contents);
  for (vector<trace_line>::iterator p = Trace_stream->past_lines.begin();  p != Trace_stream->past_lines.end();  ++p) {
    if (label != p->label) continue;
    if (contents != trim(p->contents)) continue;
    ++curr_expected_line;
    while (curr_expected_line < SIZE(expected_lines) && expected_lines.at(curr_expected_line).empty())
      ++curr_expected_line;
    if (curr_expected_line == SIZE(expected_lines)) return true;
    split_label_contents(expected_lines.at(curr_expected_line), &label, &contents);
  }

  if (line_exists_anywhere(label, contents)) {
    cerr << "\nF - " << FUNCTION << "(" << FILE << ":" << LINE << "): line [" << label << ": " << contents << "] out of order in trace:\n";
    DUMP("");
  }
  else {
    cerr << "\nF - " << FUNCTION << "(" << FILE << ":" << LINE << "): missing [" << contents << "] in trace:\n";
    DUMP(label);
  }
  Passed = false;
  return false;
}

bool trace_doesnt_contain(string expected) {
  vector<string> tmp = split_first(expected, ": ");
  if (SIZE(tmp) == 1) {
    raise << expected << ": missing label or contents in trace line\n" << end();
    assert(false);
  }
  return trace_count(tmp.at(0), tmp.at(1)) == 0;
}

int trace_count(string label) {
  return trace_count(label, "");
}

int trace_count(string label, string line) {
  if (!Trace_stream) return 0;
  long result = 0;
  for (vector<trace_line>::iterator p = Trace_stream->past_lines.begin();  p != Trace_stream->past_lines.end();  ++p) {
    if (label == p->label) {
      if (line == "" || trim(line) == trim(p->contents))
        ++result;
    }
  }
  return result;
}

int trace_count_prefix(string label, string prefix) {
  if (!Trace_stream) return 0;
  long result = 0;
  for (vector<trace_line>::iterator p = Trace_stream->past_lines.begin();  p != Trace_stream->past_lines.end();  ++p) {
    if (label == p->label) {
      if (starts_with(trim(p->contents), trim(prefix)))
        ++result;
    }
  }
  return result;
}

void split_label_contents(const string& s, string* label, string* contents) {
  static const string delim(": ");
  size_t pos = s.find(delim);
  if (pos == string::npos) {
    *label = "";
    *contents = trim(s);
  }
  else {
    *label = trim(s.substr(0, pos));
    *contents = trim(s.substr(pos+SIZE(delim)));
  }
}

bool line_exists_anywhere(const string& label, const string& contents) {
  for (vector<trace_line>::iterator p = Trace_stream->past_lines.begin();  p != Trace_stream->past_lines.end();  ++p) {
    if (label != p->label) continue;
    if (contents == trim(p->contents)) return true;
  }
  return false;
}

vector<string> split(string s, string delim) {
  vector<string> result;
  size_t begin=0, end=s.find(delim);
  while (true) {
    if (end == string::npos) {
      result.push_back(string(s, begin, string::npos));
      break;
    }
    result.push_back(string(s, begin, end-begin));
    begin = end+SIZE(delim);
    end = s.find(delim, begin);
  }
  return result;
}

vector<string> split_first(string s, string delim) {
  vector<string> result;
  size_t end=s.find(delim);
  result.push_back(string(s, 0, end));
  if (end != string::npos)
    result.push_back(string(s, end+SIZE(delim), string::npos));
  return result;
}

//:: == Helpers for debugging using traces

:(before "End Includes")
// To debug why a test is failing, dump its trace using '?'.
#define DUMP(label)  if (Trace_stream) cerr << Trace_stream->readable_contents(label);

// To add temporary prints to the trace, use 'dbg'.
// `git log` should never show any calls to 'dbg'.
#define dbg trace(0, "a")

//: Dump the entire trace to file where it can be browsed offline.
//: Dump the trace as it happens; that way you get something even if the
//: program crashes.

:(before "End Globals")
ofstream Trace_file;
:(before "End Commandline Options(*arg)")
else if (is_equal(*arg, "--trace")) {
  Trace_stream = new trace_stream;
  cerr << "saving trace to 'last_run'\n";
  Trace_file.open("last_run");
  // Add a dummy line up top; otherwise the `browse_trace` tool currently has
  // no way to expand any lines above an error.
  Trace_file << "   0 dummy: start\n";
}
:(before "End trace Commit")
if (Trace_file) {
  Trace_file << std::setw(4) << t.depth << ' ' << t.label << ": " << t.contents << '\n';
}
:(before "End One-time Setup")
atexit(cleanup_main);
:(code)
void cleanup_main() {
  if (Trace_file) Trace_file.close();
  // End cleanup_main
}

:(before "End trace_stream Methods")
string readable_contents(string label) {
  string trim(const string& s);  // prototype
  ostringstream output;
  label = trim(label);
  for (vector<trace_line>::iterator p = past_lines.begin();  p != past_lines.end();  ++p)
    if (label.empty() || label == p->label)
      output << std::setw(4) << p->depth << ' ' << p->label << ": " << p->contents << '\n';
  return output.str();
}

//: Print traces to the screen as they happen.
//: Particularly useful when juggling multiple trace streams, like when
//: debugging sandboxes.
:(before "End Globals")
bool Dump_trace = false;
:(before "End Commandline Options(*arg)")
else if (is_equal(*arg, "--dump")) {
  Dump_trace = true;
}
:(before "End Incremental Trace Print Conditions")
if (Dump_trace) return true;

//: Miscellaneous helpers.

:(code)
string trim(const string& s) {
  string::const_iterator first = s.begin();
  while (first != s.end() && isspace(*first))
    ++first;
  if (first == s.end()) return "";

  string::const_iterator last = --s.end();
  while (last != s.begin() && isspace(*last))
    --last;
  ++last;
  return string(first, last);
}

:(before "End Includes")
#include <vector>
using std::vector;
#include <list>
using std::list;
#include <set>
using std::set;

#include <sstream>
using std::istringstream;
using std::ostringstream;

#include <fstream>
using std::ifstream;
using std::ofstream;
generated by cgit-pink 1.4.1-2-gfad0 (git 2.36.2.497.gbbea4dcf42) at 2024-11-25 02:58:39 +0000