logo

Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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 e
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, four, frac, one, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Exp(e, two)
expr = Equals(Add(Mult(frac(one, two), frac(one, e)), Mult(frac(one, four), frac(one, sub_expr1))), Add(frac(one, Mult(two, e)), frac(one, Mult(four, sub_expr1)))).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left(\left(\frac{1}{2} \cdot \frac{1}{e}\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{2}}\right)\right) =  \\ \left(\frac{1}{2 \cdot e} + \frac{1}{4 \cdot e^{2}}\right) \end{array} \end{array}
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.()(2)('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: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11
8Operationoperator: 28
operands: 12
9Operationoperator: 28
operands: 13
10Operationoperator: 25
operands: 14
11Operationoperator: 25
operands: 15
12ExprTuple16, 17
13ExprTuple18, 19
14ExprTuple30, 20
15ExprTuple30, 21
16Operationoperator: 25
operands: 22
17Operationoperator: 25
operands: 23
18Operationoperator: 25
operands: 24
19Operationoperator: 25
operands: 26
20Operationoperator: 28
operands: 27
21Operationoperator: 28
operands: 29
22ExprTuple30, 36
23ExprTuple30, 35
24ExprTuple30, 31
25Literal
26ExprTuple30, 32
27ExprTuple36, 35
28Literal
29ExprTuple31, 32
30Literal
31Literal
32Operationoperator: 33
operands: 34
33Literal
34ExprTuple35, 36
35Variable
36Literal