Second order equation solver

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Second order equation
Ex second order eq.png
author Leif Roschier

Theory and background

Second order equation can be expressed as

[math]z^2+pz+q=0. \,[/math]

The shown nomogram may be used to solve z with given p and q. (Equally well solve p for given z and q...)

Construction of the nomograph

A type 10 is the block for the construction.

Generated nomograph

Second order equation
Ex second order eq.png
Generated portable document file (pdf): File:Ex second order eq.pdf

Source code

"""
    ex_second_order_eq.py
 
    Second order equation: z**2+p*z+q=0
 
    Copyright (C) 2007-2009  Leif Roschier
 
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
"""
from pynomo.nomographer import *
 
N_params_1={
        'u_min':-10.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$q$',
        'tick_levels':3,
        'tick_text_levels':2,
        'tick_side':'left'
                }
 
N_params_2={
        'u_min':-10.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$p$',
        'tick_levels':3,
        'tick_text_levels':2,
        'tick_side':'right',
                }
 
N_params_3={
        'u_min':0.0,
        'u_max':12.0,
        'function_3':lambda u:u,
        'function_4':lambda u:u**2,
        'title':r'$z$',
        'tick_levels':0,
        'tick_text_levels':0,
        'title_draw_center':True,
        'title_opposite_tick':False,
        'extra_params':[{'tick_side':'left',
                         'scale_type':'linear smart',
                         'u_min':0.1,
                         'u_max':12.0,
                         'tick_text_levels':4,
                         'tick_levels':4
                         }]
                }
 
block_1_params={
             'block_type':'type_10',
             'width':10.0,
             'height':10.0,
             'f1_params':N_params_1,
             'f2_params':N_params_2,
             'f3_params':N_params_3,
             'isopleth_values':[[2,-7,'x']]
             }
 
main_params={
              'filename':'ex_second_order_eq.pdf',
              'paper_height':10.0,
              'paper_width':10.0,
              'block_params':[block_1_params],
              'transformations':[('rotate',0.01),('scale paper',)],
              'title_str':r'$z^2+pz+q=0$'
              }
Nomographer(main_params)