logo

Expression of type Equals

from the theory of proveit.trigonometry

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import theta
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, e, frac, i, one, subtract, two
from proveit.trigonometry import Sin
In [2]:
# build up the expression from sub-expressions
expr = Equals(Abs(subtract(Exp(e, Mult(i, theta)), one)), Mult(two, Sin(frac(Abs(theta), two))))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left|\mathsf{e}^{\mathsf{i} \cdot \theta} - 1\right| = \left(2 \cdot \sin{\frac{\left|\theta\right|}{2}}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 29
operand: 7
4Operationoperator: 27
operands: 6
5ExprTuple7
6ExprTuple26, 8
7Operationoperator: 9
operands: 10
8Operationoperator: 11
operand: 15
9Literal
10ExprTuple13, 14
11Literal
12ExprTuple15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operand: 24
15Operationoperator: 20
operands: 21
16Literal
17ExprTuple22, 23
18Literal
19ExprTuple24
20Literal
21ExprTuple25, 26
22Literal
23Operationoperator: 27
operands: 28
24Literal
25Operationoperator: 29
operand: 32
26Literal
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple32
31Literal
32Variable