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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 k, m
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _phase, _t, _two_pow_t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr2 = frac(one, Exp(two, frac(_t, two)))
sub_expr3 = Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))
expr = Equals(Mult(sub_expr1, Mult(sub_expr2, sub_expr3)), Mult(sub_expr1, sub_expr2, sub_expr3)).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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\frac{1}{2^{\frac{t}{2}}} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right)\right) =  \\ \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \frac{1}{2^{\frac{t}{2}}} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\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: 32
operands: 5
4Operationoperator: 32
operands: 6
5ExprTuple8, 7
6ExprTuple8, 11, 12
7Operationoperator: 32
operands: 9
8Operationoperator: 34
operands: 10
9ExprTuple11, 12
10ExprTuple19, 13
11Operationoperator: 28
operands: 14
12Operationoperator: 34
operands: 15
13Operationoperator: 32
operands: 16
14ExprTuple17, 18
15ExprTuple19, 20
16ExprTuple40, 36, 37, 21, 38
17Literal
18Operationoperator: 34
operands: 22
19Literal
20Operationoperator: 23
operand: 26
21Literal
22ExprTuple40, 25
23Literal
24ExprTuple26
25Operationoperator: 28
operands: 27
26Operationoperator: 28
operands: 29
27ExprTuple41, 40
28Literal
29ExprTuple30, 31
30Operationoperator: 32
operands: 33
31Operationoperator: 34
operands: 35
32Literal
33ExprTuple40, 36, 37, 38, 39
34Literal
35ExprTuple40, 41
36Literal
37Literal
38Variable
39Variable
40Literal
41Literal