t.py

#!/usr/bin/env python3.
import random
import gym
import gym.spaces
from collections import namedtuple
import numpy as np
from tensorboardX import SummaryWriter

import torch
import torch.nn as nn
import torch.optim as optim


HIDDEN_SIZE = 128
BATCH_SIZE = 100
PERCENTILE = 30
GAMMA = 0.9


class DiscreteOneHotWrapper(gym.ObservationWrapper):
    def __init__(self, env):
        super(DiscreteOneHotWrapper, self).__init__(env)
        assert isinstance(env.observation_space, gym.spaces.Discrete)
        self.observation_space = gym.spaces.Box(0.0, 1.0, (env.observation_space.n, ), dtype=np.float32)

    def observation(self, observation):
        res = np.copy(self.observation_space.low)
        res[observation] = 1.0
        return res


class Net(nn.Module):
    def __init__(self, obs_size, hidden_size, n_actions):
        super(Net, self).__init__()
        self.net = nn.Sequential(
            nn.Linear(obs_size, hidden_size),
            nn.ReLU(),
            nn.Linear(hidden_size, n_actions)
        )

    def forward(self, x):
        return self.net(x)


Episode = namedtuple('Episode', field_names=['reward', 'steps'])
EpisodeStep = namedtuple('EpisodeStep', field_names=['observation', 'action'])


def iterate_batches(env, net, batch_size):
    batch = []
    episode_reward = 0.0
    episode_steps = []
    obs = env.reset()
    sm = nn.Softmax(dim=1)
    while True:
        obs_v = torch.FloatTensor([obs])
        act_probs_v = sm(net(obs_v))
        act_probs = act_probs_v.data.numpy()[0]
        action = np.random.choice(len(act_probs), p=act_probs)
        next_obs, reward, is_done, _ = env.step(action)
        episode_reward += reward
        episode_steps.append(EpisodeStep(observation=obs, action=action))
        if is_done:
            batch.append(Episode(reward=episode_reward, steps=episode_steps))
            episode_reward = 0.0
            episode_steps = []
            next_obs = env.reset()
            if len(batch) == batch_size:
                yield batch
                batch = []
        obs = next_obs


def filter_batch(batch, percentile):
    disc_rewards = list(map(lambda s: s.reward * (GAMMA ** len(s.steps)), batch))
    reward_bound = np.percentile(disc_rewards, percentile)

    train_obs = []
    train_act = []
    elite_batch = []
    for example, discounted_reward in zip(batch, disc_rewards):
        if discounted_reward > reward_bound:
            train_obs.extend(map(lambda step: step.observation, example.steps))
            train_act.extend(map(lambda step: step.action, example.steps))
            elite_batch.append(example)

    return elite_batch, train_obs, train_act, reward_bound


if __name__ == "__main__":
    random.seed(12345)
    env = DiscreteOneHotWrapper(gym.make("FrozenLake-v0"))
    # env = gym.wrappers.Monitor(env, directory="mon", force=True)
    obs_size = env.observation_space.shape[0]
    n_actions = env.action_space.n

    net = Net(obs_size, HIDDEN_SIZE, n_actions)
    objective = nn.CrossEntropyLoss()
    optimizer = optim.Adam(params=net.parameters(), lr=0.001)
    writer = SummaryWriter(comment="-frozenlake-tweaked")

    full_batch = []
    for iter_no, batch in enumerate(iterate_batches(env, net, BATCH_SIZE)):
        reward_mean = float(np.mean(list(map(lambda s: s.reward, batch))))
        full_batch, obs, acts, reward_bound = filter_batch(full_batch + batch, PERCENTILE)
        if not full_batch:
            continue
        obs_v = torch.FloatTensor(obs)
        acts_v = torch.LongTensor(acts)
        full_batch = full_batch[-500:]

        optimizer.zero_grad()
        action_scores_v = net(obs_v)
        loss_v = objective(action_scores_v, acts_v)
        loss_v.backward()
        optimizer.step()
        print("%d: loss=%.3f, reward_mean=%.3f, reward_bound=%.3f, batch=%d" % (
            iter_no, loss_v.item(), reward_mean, reward_bound, len(full_batch)))
        writer.add_scalar("loss", loss_v.item(), iter_no)
        writer.add_scalar("reward_mean", reward_mean, iter_no)
        writer.add_scalar("reward_bound", reward_bound, iter_no)
        if reward_mean > 0.8:
            print("Solved!")
            break
    writer.close()
    
   //////
  
  
  #!/usr/bin/env python3
import random
import gym
import gym.spaces
import gym.wrappers
import gym.envs.toy_text.frozen_lake
from collections import namedtuple
import numpy as np
from tensorboardX import SummaryWriter

import torch
import torch.nn as nn
import torch.optim as optim


HIDDEN_SIZE = 128
BATCH_SIZE = 100
PERCENTILE = 30
GAMMA = 0.9


class DiscreteOneHotWrapper(gym.ObservationWrapper):
    def __init__(self, env):
        super(DiscreteOneHotWrapper, self).__init__(env)
        assert isinstance(env.observation_space, gym.spaces.Discrete)
        self.observation_space = gym.spaces.Box(0.0, 1.0, (env.observation_space.n, ), dtype=np.float32)

    def observation(self, observation):
        res = np.copy(self.observation_space.low)
        res[observation] = 1.0
        return res


class Net(nn.Module):
    def __init__(self, obs_size, hidden_size, n_actions):
        super(Net, self).__init__()
        self.net = nn.Sequential(
            nn.Linear(obs_size, hidden_size),
            nn.ReLU(),
            nn.Linear(hidden_size, n_actions)
        )

    def forward(self, x):
        return self.net(x)


Episode = namedtuple('Episode', field_names=['reward', 'steps'])
EpisodeStep = namedtuple('EpisodeStep', field_names=['observation', 'action'])


def iterate_batches(env, net, batch_size):
    batch = []
    episode_reward = 0.0
    episode_steps = []
    obs = env.reset()
    sm = nn.Softmax(dim=1)
    while True:
        obs_v = torch.FloatTensor([obs])
        act_probs_v = sm(net(obs_v))
        act_probs = act_probs_v.data.numpy()[0]
        action = np.random.choice(len(act_probs), p=act_probs)
        next_obs, reward, is_done, _ = env.step(action)
        episode_reward += reward
        episode_steps.append(EpisodeStep(observation=obs, action=action))
        if is_done:
            batch.append(Episode(reward=episode_reward, steps=episode_steps))
            episode_reward = 0.0
            episode_steps = []
            next_obs = env.reset()
            if len(batch) == batch_size:
                yield batch
                batch = []
        obs = next_obs


def filter_batch(batch, percentile):
    disc_rewards = list(map(lambda s: s.reward * (GAMMA ** len(s.steps)), batch))
    reward_bound = np.percentile(disc_rewards, percentile)

    train_obs = []
    train_act = []
    elite_batch = []
    for example, discounted_reward in zip(batch, disc_rewards):
        if discounted_reward > reward_bound:
            train_obs.extend(map(lambda step: step.observation, example.steps))
            train_act.extend(map(lambda step: step.action, example.steps))
            elite_batch.append(example)

    return elite_batch, train_obs, train_act, reward_bound


if __name__ == "__main__":
    random.seed(12345)
    env = gym.envs.toy_text.frozen_lake.FrozenLakeEnv(is_slippery=False)
    env = gym.wrappers.TimeLimit(env, max_episode_steps=100)
    env = DiscreteOneHotWrapper(env)
    # env = gym.wrappers.Monitor(env, directory="mon", force=True)
    obs_size = env.observation_space.shape[0]
    n_actions = env.action_space.n

    net = Net(obs_size, HIDDEN_SIZE, n_actions)
    objective = nn.CrossEntropyLoss()
    optimizer = optim.Adam(params=net.parameters(), lr=0.001)
    writer = SummaryWriter(comment="-frozenlake-nonslippery")

    full_batch = []
    for iter_no, batch in enumerate(iterate_batches(env, net, BATCH_SIZE)):
        reward_mean = float(np.mean(list(map(lambda s: s.reward, batch))))
        full_batch, obs, acts, reward_bound = filter_batch(full_batch + batch, PERCENTILE)
        if not full_batch:
            continue
        obs_v = torch.FloatTensor(obs)
        acts_v = torch.LongTensor(acts)
        full_batch = full_batch[-500:]

        optimizer.zero_grad()
        action_scores_v = net(obs_v)
        loss_v = objective(action_scores_v, acts_v)
        loss_v.backward()
        optimizer.step()
        print("%d: loss=%.3f, reward_mean=%.3f, reward_bound=%.3f, batch=%d" % (
            iter_no, loss_v.item(), reward_mean, reward_bound, len(full_batch)))
        writer.add_scalar("loss", loss_v.item(), iter_no)
        writer.add_scalar("reward_mean", reward_mean, iter_no)
        writer.add_scalar("reward_bound", reward_bound, iter_no)
        if reward_mean > 0.8:
            print("Solved!")
            break
    writer.close()
    
    //////
    
    #!/usr/bin/env python3
import gym
import collections
from tensorboardX import SummaryWriter

ENV_NAME = "FrozenLake-v0"
GAMMA = 0.9
ALPHA = 0.2
TEST_EPISODES = 20


class Agent:
    def __init__(self):
        self.env = gym.make(ENV_NAME)
        self.state = self.env.reset()
        self.values = collections.defaultdict(float)

    def sample_env(self):
        action = self.env.action_space.sample()
        old_state = self.state
        new_state, reward, is_done, _ = self.env.step(action)
        self.state = self.env.reset() if is_done else new_state
        return (old_state, action, reward, new_state)

    def best_value_and_action(self, state):
        best_value, best_action = None, None
        for action in range(self.env.action_space.n):
            action_value = self.values[(state, action)]
            if best_value is None or best_value < action_value:
                best_value = action_value
                best_action = action
        return best_value, best_action

    def value_update(self, s, a, r, next_s):
        best_v, _ = self.best_value_and_action(next_s)
        new_val = r + GAMMA * best_v
        old_val = self.values[(s, a)]
        self.values[(s, a)] = old_val * (1-ALPHA) + new_val * ALPHA

    def play_episode(self, env):
        total_reward = 0.0
        state = env.reset()
        while True:
            _, action = self.best_value_and_action(state)
            new_state, reward, is_done, _ = env.step(action)
            total_reward += reward
            if is_done:
                break
            state = new_state
        return total_reward


if __name__ == "__main__":
    test_env = gym.make(ENV_NAME)
    agent = Agent()
    writer = SummaryWriter(comment="-q-learning")

    iter_no = 0
    best_reward = 0.0
    while True:
        iter_no += 1
        s, a, r, next_s = agent.sample_env()
        agent.value_update(s, a, r, next_s)

        reward = 0.0
        for _ in range(TEST_EPISODES):
            reward += agent.play_episode(test_env)
        reward /= TEST_EPISODES
        writer.add_scalar("reward", reward, iter_no)
        if reward > best_reward:
            print("Best reward updated %.3f -> %.3f" % (best_reward, reward))
            best_reward = reward
        if reward > 0.80:
            print("Solved in %d iterations!" % iter_no)
            break
    writer.close()
    
    ////
    
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%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /YQYTWD+CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 65 /A put
dup 71 /G put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 86 /V put
dup 97 /a put
dup 13 /gamma put
dup 58 /period put
dup 25 /pi put
dup 115 /s put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F4_0 /YQYTWD+CMMI10 1 1
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pdfMakeFont
%%BeginResource: font NUMAFF+CMMI7
%!PS-AdobeFont-1.0: CMMI7 003.002
%%Title: CMMI7
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI7.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI7 known{/CMMI7 findfont dup/UniqueID known{dup
/UniqueID get 5087382 eq exch/FontType get 1 eq and}{pop false}ifelse
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11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /NUMAFF+CMMI7 def
/FontBBox {-1 -250 1171 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI7.) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 107 /k put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F5_0 /NUMAFF+CMMI7 1 1
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pdfMakeFont
%%BeginResource: font SOSTRQ+CMR10
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /SOSTRQ+CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 91 /bracketleft put
dup 93 /bracketright put
dup 61 /equal put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F6_0 /SOSTRQ+CMR10 1 1
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pdfMakeFont
%%BeginResource: font YMRXOK+CMR7
%!PS-AdobeFont-1.0: CMR7 003.002
%%Title: CMR7
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR7.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR7 known{/CMR7 findfont dup/UniqueID known{dup
/UniqueID get 5000790 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /YMRXOK+CMR7 def
/FontBBox {-27 -250 1122 750 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR7.) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 61 /equal put
dup 49 /one put
dup 43 /plus put
dup 50 /two put
dup 48 /zero put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /YMRXOK+CMR7 1 1
[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
  /.notdef/.notdef/.notdef/plus/.notdef/.notdef/.notdef/.notdef
  /zero/one/two/.notdef/.notdef/.notdef/.notdef/.notdef
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pdfMakeFont
%%BeginResource: font DZZUCU+CMSY7
%!PS-AdobeFont-1.0: CMSY7 003.002
%%Title: CMSY7
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY7.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY7 known{/CMSY7 findfont dup/UniqueID known{dup
/UniqueID get 5096648 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /DZZUCU+CMSY7 def
/FontBBox {-15 -951 1251 782 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY7.) readonly def
/FullName (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
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readonly def
currentdict end
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  /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef
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pdfMakeFont
%%BeginResource: font YQJSDJ+CMEX10
%!PS-AdobeFont-1.0: CMEX10 003.002
%%Title: CMEX10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMEX10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMEX10 known{/CMEX10 findfont dup/UniqueID known{dup
/UniqueID get 5092766 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /YQJSDJ+CMEX10 def
/FontBBox {-24 -2960 1454 772 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMEX10.) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 88 /summationdisplay put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F4_0 /YQYTWD+CMMI10 1 1
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pdfMakeFont
%%BeginResource: font SOSTRQ+CMR10
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /SOSTRQ+CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 91 /bracketleft put
dup 93 /bracketright put
dup 61 /equal put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
readonly def
currentdict end
currentfile eexec
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cleartomark
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/F6_0 /SOSTRQ+CMR10 1 1
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pdfMakeFont
%%BeginResource: font RAZVEJ+MSBM10
%!PS-AdobeFont-1.0: MSBM10 003.002
%%Title: MSBM10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name MSBM10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/MSBM10 known{/MSBM10 findfont dup/UniqueID known{dup
/UniqueID get 5031982 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /RAZVEJ+MSBM10 def
/FontBBox {-55 -420 2343 920 }readonly def
/PaintType 0 def
/FontInfo 7 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name MSBM10.) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 69 /E put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F15_0 /RAZVEJ+MSBM10 1 1
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pdfMakeFont
%%BeginResource: font XDJWFC+CMSY10
%!PS-AdobeFont-1.0: CMSY10 003.002
%%Title: CMSY10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMSY10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup
/UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /XDJWFC+CMSY10 def
/FontBBox {-29 -960 1116 775 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMSY10.) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 106 /bar put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F16_0 /XDJWFC+CMSY10 1 1
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pdfMakeFont
%%BeginResource: font NUMAFF+CMMI7
%!PS-AdobeFont-1.0: CMMI7 003.002
%%Title: CMMI7
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI7.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI7 known{/CMMI7 findfont dup/UniqueID known{dup
/UniqueID get 5087382 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /NUMAFF+CMMI7 def
/FontBBox {-1 -250 1171 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI7.) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 107 /k put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F5_0 /NUMAFF+CMMI7 1 1
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