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Expression of type Mult

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.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
expr = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Mult(frac(one, Exp(two, frac(_t, two))), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))))
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())
\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)
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',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 27
operands: 1
1ExprTuple2, 3
2Operationoperator: 29
operands: 4
3Operationoperator: 27
operands: 5
4ExprTuple15, 6
5ExprTuple7, 8
6Operationoperator: 27
operands: 9
7Operationoperator: 23
operands: 10
8Operationoperator: 29
operands: 11
9ExprTuple35, 31, 32, 12, 33
10ExprTuple13, 14
11ExprTuple15, 16
12Literal
13Literal
14Operationoperator: 29
operands: 17
15Literal
16Operationoperator: 18
operand: 21
17ExprTuple35, 20
18Literal
19ExprTuple21
20Operationoperator: 23
operands: 22
21Operationoperator: 23
operands: 24
22ExprTuple36, 35
23Literal
24ExprTuple25, 26
25Operationoperator: 27
operands: 28
26Operationoperator: 29
operands: 30
27Literal
28ExprTuple35, 31, 32, 33, 34
29Literal
30ExprTuple35, 36
31Literal
32Literal
33Variable
34Variable
35Literal
36Literal