Using Maxima with Mac OS X in Emacs imaxima Mode

Maxima is a computer algebra system written in common lisp.  For me, it is an alternative to Mathematica. To install maxima with Mac OS X, I use Homebrew.  However, maxima is not in the official repository of Homebrew, so we cannot install it simply using command like brew install maxima.  Instead, we need to register the repository <code>homebrew/science</code> before installing:

brew tap homebrew/science
brew update
brew upgrade
brew install homebrew/science/maxima

Then, open the ~/.emacs file and add two lines to load imaxima mode:

(add-to-list 'load-path "/usr/local/Cellar/maxima/5.25.1/share/maxima/5.25.1/emacs")
(require 'maxima)

In Emacs, launch Maxima in imaxima mode by M-x imaxima. Then you can do what ever you want!


Google Protocol Buffer: Custom Options with Repeated Fields

We encountered a question about Google protocol buffer: could we create a custom option which has a repeated decoration?

The protocol buffer compiler, protoc, answers: no.

However, it is OK to create an option with a message type, and the message could contain a repeated field. Here follows an example program.

The content of learn.proto:

import "google/protobuf/descriptor.proto";

message Something {
  repeated int32 a = 1;

extend google.protobuf.FieldOptions {
  optional float my_field_option = 50002;
  optional Something my_another_field_option = 50003;

message MyMessage {
  optional string my_field = 1
    [(my_field_option) = 1.1];
  optional string my_another_field = 2
    [(my_another_field_option) = { a : [111, 222, 333] } ];

The content of

#include <iostream>
#include <google/protobuf/descriptor.h>
#include "learn.pb.h"

int main() {
  MyMessage m;
  const ::google::protobuf::Descriptor* msg_desc = m.descriptor();
    const ::google::protobuf::FieldDescriptor* field_desc =
    const ::google::protobuf::FieldOptions& field_options =
    float option = field_options.GetExtension(my_field_option);
    std::cout << "my_field_option = \n" << option << "\n";
    const ::google::protobuf::FieldDescriptor* field_desc =
    const ::google::protobuf::FieldOptions& field_options =
    Something option =
    std::cout << "my_another_field_option = \n"
              << option.DebugString() << "\n";

  return 0;

The content of Makefile:

learn : learn.pb.h
	g++ -o learn -lprotobuf && ./learn

learn.pb.h : learn.proto
	protoc learn.proto --cpp_out=. \

The execution result is as so:

my_field_option =
my_another_field_option =
a: 111
a: 222
a: 333

Few more words here. The field option in protocol buffer has been inherited by the Go programming language and becomes struct tag. As described in the Go language specification:

A field declaration may be followed by an optional string literal tag, which becomes an attribute for all the fields in the corresponding field declaration. The tags are made visible through a reflection interface but are otherwise ignored.

As you see, struct tags in Go are restricted to be strings — no repeated decoration, no message type.